DVD/CD-RW doesn't seem to be working

Toshiba/Samsung TS-H493 48x32x48 CD-RW/16x DVD-ROM is an old combo drive.  It may need upper and lower filters cleared and or firmware updated.

http://downloads.dell.com/rmsd/TSST_TS-H493B-HH-SATA-48X-CD_A03_R201947.EXE

Custom Instructions for TSST_TS-H493B-HH-SATA-48X-CD_A03_R201947.EXE:
Download
1. Click Download File, to download the file.
2. When the File Download window appears, click Save this program to disk and click OK.
The Save In: window appears.
3. From the Save In: field, click the down arrow then click to select Desktop and click Save.
The file will download to your desktop.
 4. If the Download Complete window appears, click Close.

The file icon appears on your desktop. Install (Windows XP and Vista Users)
1. Save all work and be prepared to reboot the system after flashing the drive.
Double-click the new icon on the desktop labeled TSST_TS-H493B-HH-SATA-48X-CD_A03_R201947.EXE.
2. The Self-Extracting window appears and prompts you to extract or unzip to "C:\DELL\DRIVERS\R201947".
Write down this path so the executable (i.e. Setup.exe) file can be found later.
3. The Self-Extractor window appears.
4. Click OK. 5. After completing the file extraction, if the Self-Extractor window is still open, close it.
6. The Windows Flash utility, SFDNWIN, for the TSST TS-H493B drive will automatically launch.
7. If a "Drive not found" message pops up, then the system is not detecting the TSST TS-H493B drive.
Check to make sure the TSST TS-H493B drive is properly installed.
8. The SFDNWIN flash utility window will appear.
Click on the round folder icon on the extreme top left corner of the SFDNWIN window.
9. Navigate to the folder "C:\DELL\DRIVERS\R201947". 10. Select 493BD400.BIN.
11. Click on the "Flash to Drive" icon next to the folder icon on the top left of the SFDNWIN window.
(It is the 2nd of the three icons on the top left of the SFDNWIN window).
12. Wait for the flash process to complete.
13.Acknowledge reboot request to reboot system.

Thank you for this answer. Although I don't know anything about this, your instructions look like they are very clear and I should be able to follow them. Before I implement this ... could you take a look at a file from a tool I ran last night called Nero Info Tool and let me know if there is anything that jumps out at you? 

Where do I find firmware upate for this. I went to Dell.com but I couldn't find anything. I find that site really confusing and difficult to get to where you want to go so maybe I wasn't in the right place. I never used to have any trouble until the warranty ran out on my machine and now it's almost like they don't want you to find anything on older systems.

Apparently I'm doing something wrong.

I get a window SFDNWIN and my TSST drive is listed in the window. When I click on that first circle, top left, I get a box "This firmware is not compatible with the selected drive." 

C\Dell\Drivers\R201847 contains two files: DOS and WIN. In each there is 493BD400.BIN and an .exe file.

DELL drives are TSST TS-H493B and you have TSST TS-H493A

http://support.lenovo.com/us/en/downloads/ds001288

This is the drive my computer came with.

Anyway, I downloaded the 493A file from the link you provided above and it still won't work. 

I followed the instructions below and the exact same thing happened as when I followed the instructions you laid out for me in the email. 

I get the SFDNWIN box, click on the far left-top circle, a window opens wtih Look in: DOS and in the box below it has the file 493BD400.BIN. I hi-lite it and it appears in the File Name box below with Type of File: DOWNLOAD FILE {*.BIN}. When I click Open it says "This firmware is not compatible with the selected drive."

Extracting the package
======================
Windows Vista
-------------
1.  Click Start, then click Start Search.
2.  Type tsst_ts493a_ib03.exe in the search field, then click Search
    Everywhere. This will locate the file you just downloaded.
3.  Double-click the tsst_ts493a_ib03.exe icon. You may see a dialog
    stating "A program needs your permission to continue". If you
    see this dialog, click Continue.
4.  Click Next.
5.  Click I accept the terms in the license agreement.
6.  Click Next.
7.  Ensure that "Save files in folder" is set to
    C:\SWTOOLS\FIRMWARE\TSST\TS-H493A.
8.  Click Next. The necessary files will be extracted to your hard drive.
9.  Click Finish.

Applying the package
====================

Windows Vista ------------- 1. Click Start, click All Programs, click Accessories, then click Run. 
2. Type C:\SWTOOLS\FIRMWARE\TSST\TS-H493A\TS-H493A_IB03.exe, then click OK. The firmware upgrade utility will proceed automatically. 
3. When you see the "Download OK!! Restart WINDOWS" message, click OK. 
4. The firmware upgrade will be applied when the system restarts.

The drive is bad then. None of the available firmware even recognize it as a working drive. Since you have 2 drives you could try swapping their cables and booting from the other drive.

I'm not trying to be argumentative, but just want to make sure you have all the facts to advise me with. I figured out how to go into my system (F12) and run the Dell diagnostics. I started out with the TSST drive. Device Quick Check, Seek Test and Built-in Self Test all passed; with Read Test showing NA.

I don't know for sure what the Read Test NA signifies, but if the drive is shot would the other tests have come back with PASS?

I also tested everything else, individually, and everything passed. The only thing I didn't let run to finish was the HD test because it was just taking too long; however, it was over half finished when I finally used the ESC and there were no problems at that point. I had used another tool just a couple of weeks ago, HD Tune, to test the HD with and it passed 100%..