Since you are on a PC in a public library which limits the things you can do and the programs you must use, you should just buy a USB with the flavor of Linux you want. I suggest Linux Mint . I am hoping that whichever PC you are using has at least 4 GB of RAM. .

What about the MS Office 2007 that is not recognized either. works fine on .

so it is good, so your OS is corrupted. as I stated,  if the disc is not seen in , 3 places you have corruption there.

1:explorer, device manager, and last disk manager, LOOK THERE FIRST. 

If disk manager shows no driver, the DVD drives is dead or bad drivers  for DVD or bad corrupted OS present.

As I said, the Linux disk does work on my really old Optiplex, GX620.

That is why I thought about switching the dvd drives. 

no that would be last, not first, what is first let me tell that one more time.

Drives 2 cables reseated first. always do that first,

then F2 bios, turn off safe boot, first.  if not turned off you will never ever boot any DVD, CD or the like.

Failure to boot a good DVD. (known good) Linux tested on 2 or 3 good PCs, not bad PC or infected.

Caused of non boot DVD.

1: bad DVD  drive.

2: BIOS set up wrong. safeboot off and use F12.

3: cables fell off or loose both on DVD drive rear.

did you buy a used DVD drive off of fleabay? and expect it to be good, many are not.

power on PC and hammer F12, (after F2 safeboot is off)  the Drive must show up or the drive is bad.
the  the optical drive must show up in F12. OK> ?

The Linux disk also installed(inserted in tray) on an old HP which happens to have the same model of dvd drive as the OptiPlex, that is not working. (the disk is not working or the PC?) I can not tell what that  line of text means. why test a DVD disk on a dead PC? what is there to learn here?

NO HP Model stated, all mY HP DVD works here. a z600 !

so the DVD is IS dead on 2nd PC?, try this DVD on a 3rd PC, to be sure,  none if these PC are new.

Did you burn these DVD your self using DVD-R or DVD+R,  media?

and test it on many PC to be sure its solid burn, !?  (I use ImgBurn free, and never made coaster yet.

(coaster means useless optical  disk)

Here is  GREAT 755 BIOS A22 fresh,,, youtube video review. set this page to legacy yet?(Sata OPERATION)

turn on ALL SATA ports to ON, oK, try to.

next under, integrated  NIC (network) PICK  "ON" and never, PXE, or PC will not boot. to HDD or DVD.

then set, under USB controller.,  to  ON,, and DO NOT PICK, NO BOOT. !

in the same USB vain, turn on all USB  ports, OK? each line turn them on front and rear.

under security , no passwords set on SATA 0 to 3 (all 3 ports set to no.)
TPM turned OFF NEXT.

UNDER FAST BOOT, TURN THAT  OFF. (means verbose BIOS error reports and longer checking)

BEST I CAN TELL A22 has no  safeboot feature,  (UEFI class lame, so is good this, missing good.)

this video is a treasure,  dell does not document bios or does so , in tiny bits, never all.. and not for A22. version.

in the video see BOOT sequence,  in this video his drives are missing,

yours must not be missing and the DVD drive must show up and BE SET FIRST BY YOU, oK.

now rule #1, this PC unlike newer PC, has El Torito spec, boot devices, (DVD or USB)

that means the DVD will not boot unless you hammer the space bar.  (intel rules back then, and later removed)

the acid test is to remove the HDD cables, and have only DVD and Linux in the tray. (this is just a test)

then power on and hit F12 see if the DVD shows and then pick it, if not then...

then tap the Space bar as the PC boots and the DVD will then boot.  (El Torito rules there)

PXE off disabled, and HDD cables pulled will force the DVD to boot,  and space bar hit. by you.... tap tap tap bam boots the DVD, if it is good and the  drive.

if this work , you know what to do next, right? answer is get the boot ORDER RIGHT.

I think I covered every  BIOS reason on this PC to not boot DVD.  above.

i installed a different hard drive last night, putting the old hard disk in slot #2. Couldn’t install windows because it is not NTFS so I stuck the linux disk in and it installed perfectly. I was going to install it next to windows, but if I can figure out how to get to the second disk it will be fine. I will try reconnecting them in the order you noted but can’t see why that matters if the computer is off. Do I start and stop the computer in between?

I always go to ebay first. If it doesn’t work the seller almost always just sends a refund, rather than get a bad review I assume.

I pity the eBay seller that sells you anything. He probably sends you a perfectly working part and just because you don't know what you are doing he has deal with the mess. shaking my head.

.

Couldn’t install windows because it is not NTFS 

This is not the issue.  Advanced format drives require F6 mass storage drivers.

Sata Operation needs to be set to AHCI.

You then boot from OEM

System Builder DVD.  However most win7 8 10 disks will require the region set on the drive before it will show F12 bootable.

https://www.newegg.com/microsoft-windows-10-pro-64-bit-reinstall-recovery-disc-only-no-license-key-included/p/N82E16832350238

This is why I always recommend OEM System builder DVD disk and USB 2.0 optical drive.  Cannot be USB3 on older models.

https://www.bestbuy.com/site/lg-8x-external-usb-2-0-blu-ray-disc-double-layer-dvdrw-cd-rw-disc-rewriter-black/9243009.p?skuId=9243009

https://support.microsoft.com/en-us/help/952951/error-a-required-cd-dvd-device-driver-is-missing-when-you-start-window

This error can occur if one or more of the following scenarios are true: 

• The CD/DVD drive may not be compatible with Windows 7 or Windows Vista
• The CD/DVD media may be damaged or dirty or does not have region set.
• Your CD/DVD drive may be incompatible with the F6 Microsoft AHCI driver (msahci.sys)

https://www.seagate.com/support/kb/error-installing-windows-7-on-advanced-format-disk-drives-218571en/

https://www.dell.com/support/article/us/en/04/sln146650/system-image-support-for-advanced-format-hard-drives-on-dell-business-client-notebooks-and-desktops?lang=en

https://www.dell.com/support/article/us/en/04/sln297954/dell-computers-tested-for-windows-10-november-2019-update-and-previous-versions-of-windows-10?lang=en

Another Win10 DVD suggestion as it's a newer version:

Edited:  Link removed as I didn't know item was pirated.

I absolutely reject and DO NOT RECOMMEND the EBAY DVD you suggest as this is NOT official microsoft media its pirated burned disk.  The OEM System builder disk from Newegg is an actual DVD from microsoft.  It won't ever go bad like a burned DVD would.

The reason older units have a hard time reading 1809 1903 1909 media is because its DUAL LAYER DVD aka the install.wim and ISO is larger than standard DVD 4.7 gigs. install.wim file is now too big to fit on FAT32 media being over 4 gigs.  Unfortunately especially with older systems USB3 and UEFI require FAT32.  EXFAT and NTFS  are not supported which is why a fat32 usb flash drive does not allow the install.wim file to fit.

dism /Split-Image /ImageFile:"c:\temp\install.wim /SWMFile:"c:\temp\install.swm" /FileSize:3800

https://www.dell.com/support/article/us/en/04/sln313422/windows-10-iso-contains-wim-file-that-is-big-for-fat32-file-system?lang=en

https://www.newegg.com/microsoft-windows-10-pro-64-bit-reinstall-recovery-disc-only-no-license-key-included/p/N82E16832350238

A full version of the Windows operating system is provided  with the Microsoft System Builder DVD.

One disk can be used to recover ANY machine with valid licence legally.

The EBAY disk is neither legal nor supported by microsoft.

If your drive does not recognize the media you should use USB 2.0 optical drive.

USB3 versions won't work properly on older systems.

The reason I recommend this specific model is that it comes with Cyberlogic Power DVD software which you will want as that is removed from Windows 8 and 10.

https://www.bestbuy.com/site/lg-8x-external-usb-2-0-blu-ray-disc-double-layer-dvdrw-cd-rw-disc-rewriter-black/9243009.p?skuId=9243009

Being USB 2.0 and a burner it also supports DUAL LAYER DVD's that are required for windows 10  1809 1903 1909.

Being USB 2.0 also means it F12 boot works with all dell models desktop or laptop from 2006 to 2020 and beyond with windows XP/VISTA/7/8/10

Also works with most linux including Fedora, Redhat, Ubuntu, SUSE etc.

 installed a different hard drive last night, putting the old hard disk in slot #2.

Couldn’t install windows because it is not NTFS  Windows 10? this is false, this statement 100%

you erase the disk first, so setup.exe does not block you, windows installer does not like, 2 things,

wrong formatted drives ( over 100 alien formats not allowed even apple fmt) and not erased first.

the installer even tries to protect data. it it can even see you have data there it will BALK, by DESIGN.

erase the HDD first (computer basics 101) and windows installed all by it self no need for you do know anything, it just does so automatically from any erased HDD or SSD,  learn that. please.

so I stuck the linux disk in and it installed perfectly.

That is because(no Linux stated) does not check for data first. (new Linux does ) it just finds space and lays in new partitions,  yes, I am Linux person. too) run Ubuntu V17 here, and now has blocks to W10 formats.  does.

'

I was going to install it next to windows, but if I can't figure out how to get to the second disk it will be fine.

you BIOS does not support dual booting NOW, w10 does not. no OS stated, in your posts.

BIOS is NOT A BOOT MANAGER AT ALL forget that.

in the old legacy days the BCD store, controls the boot, see editor by same name

in Linux GRUB does this, Grub can boot many OS,  but now W10, for sure 64bit and secure boot on.

I will try reconnecting them in the order you noted but can’t see why that matters if the computer is off.

huh?

Do I start and stop the computer in between?  , in between what?, add one more word at least.

why tell about ebay here, and your rule is antidotal at best.. and has nothing to do with OS installs.

if you want to dual boot any PC start a post with that as a topic (and name  at lest 2 OS exactly by name and Version or there will never be any answers)

or better yet learn to read posst here or at Microsoft forum, 10,000 post there and here tells you NO. (w10)

to run w10 you need to run the other OS as VTx  virtual machine image. with A CPU that has that feature.

and can be done both ways, Linux with VT to windows or the reverse. (and lots of  rules you do not know yet)

not sure what you are doing or trying, not me.... not at all.

DO NOT ever post any media of any kind to this form that is pirated, it will be deleted OK.

for deity (random) sake, what in the world are you doing, ?

what do you have now and where do you wish to go,  not stated at all clearly. pick a goal as stated it.

then tell what OS you have now and version or if dead now OS, and what version you want to run. name and version, like Window 10 64bit.

The MICROSOFT.com web site has the W10 usb maker ISO there and costs zero dollars to get.

and run it for 30 full days free,   why is that so hard to know?  and a free license is possible if you can prove w7 owner ship . 

to install w10 from MS (get the dual version 32/64 iSO ) build the stick using the free MS ISO stick builder.

set the PC bIOS to 100% legacy mode. safeboot  disable for sure !!! inside F2 BIOS.

then boot the stick ( USB ports enable, USB booting enabled, in BIOS F2) 

and first erase any HDD first. learn how to erase disk, did  you know, that the w10 installer can NOT erase all disks, of 100+ of formats! in the wild, that is a fact. learn that 1st. (I can list all 100 to you but why)

W10 installs automatically to any pure erased disk, no issues EVER>

if the booted installer fails to see your disk or does not like your disk take that to the bank it is a fact .

bad disk or NOT ERASED First (we are booted from USB stick do not use DVD, as they are too slow and problematic for sure this old)

if you have too many partitions the installer also fails.  (cured only with GPU UEFI  mode set PC'S)

do you even know the difference what a formatted disk and erased is? (erased means 100% pure empty)

the latter contains NO FORMAT AT ALL, period.  and all Microsoft OS installed to any real erased HDD./SSD.

learn to erase and now, I use KILLDISK.exe free. works perfect every time. (but needs and OS to run)

my guess is you have no working OS now.

there are more tricky ways sure, one can boot a w10 install disk and go to command prompt and use.

USING DISKPART  utility. (this uses only MS software and is FREE)

w10 now has a new remove everything feature, after 40 year waiting MS gets head out of the sand. (non geek ways) google that to learn but W10 must be running now. to do that.

• Click Start Bottom, and click Settings
• Click Update and Security
• Click Recovery, find Reset this PC, and click Get Started
• Choose an option between "Keep my files" and "Remove everything"

but you don't have working w10 PC to erase disk 2.

here is the boot media installer answer here,  how to erase any hDD.

advanced option, then click command prompt from boot installer mode.

at the command prompt do the steps here with DISKPART clean, (no need to do clean all)

when you boot the w10 install media you get choices, here is page 1.

now a click list

1. boot w10 installer from USB port
2. click repair your computer
3. click advanced.
4. click command prompt
5. (use commands to pick a drive if only one drive present (hint) no brainer. actions next

this lame page looks like this with old or dead OS there. your s will shows unallocated space on  drive.bingo.

if and only if the OS installer likes what it sees there, the delete key works too. there.  if not not.

not means alien

other errors are mbr format not possible on UEFI enabled BOIS ( so change it)

error 2, cant have dynamic volumes there.

error 3, contains important data working, do as you please.

error 4, GPT volume not allowed

error 5, going deeper than 4 partitions,,  MBR 4 primary max. GPT is 128 parts.

there are more errors possible for sure bad hdd, or  corrupted partition and frankly endless, really

erase the drive,  and start new.

I use killdisk on my windows 7 PE live media disk, or my cool TODO disks, same.

on a 2nd PC,  that runs perfectly and HDD not bad, the disk can be erased in DISK MANAGER easy.

right click disk there (2nd good PC) and pick delete VOLUME,  gone it is.

there are endless ways to erase, some of the above are very common . learn how first. for sure.

vast persons send new HDD back for refund not  a clue what erase means or how.