Creating Windows 7 bootable USB drive

Images are available for Windows 10 -- and some for Windows 8.  For Windows 7, you'll need to call Dell to see if they'll sell you a set of recovery media - there is no official channel for obtaining an ISO of Windows 7.

Have you tried resetting BIOS to the factory defaults before trying to install Win 7 from the Dell disk?

You should have a sticker somewhere on the PC with your unique product key for Win 7, but if you use a Dell OEM disk with the exact same version of Win 7 (Home or Pro) to install Windows on the new HDD, it shouldn't even ask for the key.

You can always look on eBay etc. You only need to get a DVD that has the same version of Windows. Make sure to get one with Win 7+SP1, but you don't have to  buy one with an activation key, assuming you buy a Dell OEM disk and/or have the sticker with your product key.

The Dell OEM Windows Reinstallation disk should be bootable.

But if there's a problem with BIOS setup (eg, a corrupt or incorrect setting) you may not be able to boot from it, or maybe Windows setup is having trouble recognizing the hardware because there's a problem in BIOS, which is why I suggested you reset it to the defaults... You can copy down all the current settings first, just to be safe...

If you put the Windows DVD in the drive, reboot and immediately press F12, you should see a menu that allows you to boot from the DVD without changing the boot sequence in BIOS.

EDITED

I haven't reset the BIOS, no.  I thought about it, but decided I wanted to avoid any potentially unnecessary changes until after I tried running the Windows repair tool first, if I could.

And I wasn't going to install Windows - I just wanted to boot from the DVD so that I could launch the repair tools that way, since I couldn't get them to launch from my PC.  Can you only install from the Dell OEM disks and not boot from them? It showed the Windows logo for an hour before going to a black screen, so I assumed the disk might be bad, but if it's not bootable that might explain it.  

So, my question now is, how can I get a Windows 7 ISO from Dell, that I can put on a USB drive?

Any Windows 7 ISO should do. You don't need one from Dell, but you can a get Dell-specific one on eBay for a nominal sum. 

Yeah, the F12 method is what I was using to try booting from the DVD.  I'll go ahead and try resetting the BIOS to default, though...fingers crossed.

Ok, so resetting the BIOS to default had no impact.  Next, I had the idea of making an ISO off the Dell install disk I had, and then using Rufus to load that ISO onto a USB drive to make it bootable.  Did that, started up the PC with the USB configured as the boot drive this morning.  It loaded files, showed the Windows logo, then went to a black screen (no mouse cursor)...and was there for a half hour before I needed to leave for work.  Hoping it's going to eventually load something...will see when I get home tonight.

You may be back to a failed hard drive. So unless you install a new one, you may be stuck...

First step run F12 preboot diagnostics. Run all checks including any extended tests

https://www.youtube.com/watch?v=WDpvQ3qwy1c&index=12&t=8s&list=PL1RkaknDn7v-Ucth4gt0U3BHVSY7oNkWr 

I suspect you may have a failed HDD or a faulty RAM module. 

Let us know whether the tests pass or not.

Regarding Windows Installation Media the XPS 8100 is an Early 2010 Model meaning all XPS 8100's are out of warranty. Windows 7 has also Reached End of Mainstream Support and End of OEM sales. Microsoft only allow Dell to provide Windows 7 installation .isos for new (2015-2016) systems which are sold with Windows 10 Pro OEM Downgrade Rights.

Microsoft have listened to our feedback on the forums regarding Windows Installation Media. I've been highlighting issues such as yours for quite some time. With Windows 10 you can Download the latest installation .iso direct from Microsoft. You may clean install Windows 10 with your Windows 7 OEM Product Key. Ignore any remarks you read online about a 1 year promotional period, this was extremely poorly worded marketing. Your Windows 7 OEM key will still activate Windows 10 on your XPS 8100 even if you have never installed Windows 10 before.

Note the XPS 8100 has a Legacy BIOS so use the "MBR partition scheme for BIOS" when making a Bootable USB.

For more details see here:

http://dellwindowsreinstallationguide.com/download-windows-10-oem-and-retail-iso/ 

https://www.youtube.com/playlist?list=PL1RkaknDn7v-Ucth4gt0U3BHVSY7oNkWr 

Its a bit cumbersome to Download Windows 7 and update the installation media. I hence recommend going to Windows 10. If you want the Windows 7 .iso there is a means of Downloading it from Microsoft. See here for details:

http://en.community.dell.com/support-forums/software-os/f/3524/t/19999620 

Yeah, I ran diagnostics at the beginning of all this, and it came back with the hard drive error code.  I guess I was hoping that I could still run Windows startup repair against it, in case it was a minor issue, since the drive is still listed in the BIOS so it's not completely dead.  However, since it looks like booting from the install DVD and a USB drive are both just ending up in a black screen (which is different from the blue partly loaded repair startup screen I got when booting from the HD, but still stuck either way)...I guess that's not going to work.  I didn't realize that a bad hard drive could prevent Windows from loading from a disk, but googling around indicates that can happen.  Soo.....yeah, probably not much else I can do at this point without a second, new hard drive.  

Startup repair DOES NOT FIX physically damaged drives.  in general I cannot think of any instance where the "repair" actually worked EVER even with a working non damaged drive.

Just to update, I got a new HDD and installed it.  Windows still didn't boot up from USB or DVD drive - it would start, and then go to a black screen with no cursor.  So, I disconnected the power/data cables from the original bad drive and retried.  This time, Windows installation screens came up and I was able to install Windows 7 on the new drive (working around one issue where I needed to download/install drivers for the Win install to complete successfully - it initially said it couldn't install Windows on my hardware).  Once Windows was installed, I installed some updates to get to SP1, and then turned off the PC and tried plugging in the power/data cables to the original HDD again.  This time, when I restarted (specifying that the new HDD should be booted), Windows came up.  I couldn't access the original HDD because of an error - Windows said it needed to be formatted.  So I restarted into safe mode command prompt and then ran chkdsk /f on the original HDD.  I had to run it twice - I still couldn't access it after the first run.  After the second run, however, I was able to see files on it again.  I then rebooted and tried specifying the original HDD for booting.  This time it did come up and successfully ran Windows startup repair, though it couldn't find anything to fix (presumably because chkdsk already fixed it?).  

So...I think I'm past the worst of it, hopefully, and just need to clone everything to the new hard drive now.  So apparently, the problems I was having with booting Windows from a DVD/USB were due to a bad disk being connected, screwing up Windows' startup attempts.