Computer does not recognize CD/DVD drives

Did you try a restore point?

http://windowshelp.microsoft.com/Windows/en-US/help/517d3b8e-3379-46c1-b479-05b30d6fb3f01033.mspx

Try opening the case and disconnecting the drives from the motherboard.
Boot up.
Shut down.
Reconnect the drives and check all cable connections are tight.
Boot up again.

Also, if it's a new PC, it should be under warranty from Dell. Depending on the warranty level, they should ship you new parts or even have someone come out and replace the parts. Give them a call at +18006249896

You could also try restoring the computer back to it's original factory defaults (this will erase any changes you have made):

1. Restart the computer. To do this, click Start, click the arrow next to the Lock button, and then click Restart.
 
2. As the computer restarts, press the F8 key until the Advanced Boot Options menu appears on the screen.

3. Press the (Down Arrow) to select Repair Your Computer on the Advanced Boot Options menu, and then press Enter.
 
4. Specify the language settings that you want, and then click Next.
 
5. Log in as a user who has administrative credentials, and then click OK.
 
6. Click Dell Factory Image Restore.
 
7. In the Dell Factory Image Restore window, click Next.
 
8. Click to select the check box for Yes, reformat hard drive and restore system software to factory condition.
 
9. Click Next. The computer is restored to the default factory configuration.
 
10. When the restore operation is completed, click Finish to restart the computer.

Check bios first see if the media has any error or not detected in there. If they are OK in bios, you might try to remove upper and lower filters, change cables if needed.

As HighTechGeek said, call Dell's hardware support line - 1-800-624-9896

I'm am sorry to say none of the suggestions fixed the problem of the computer not recognizing the two DVD Burners installed on my new Dell computer using Windows Vista.
I did some research on my own and there is a registery hack that is reported to fix the problem.  I have not had time to try this fix.
I thank you all for trying and giving me suggestions to try and fix this problem.
Digital Dave

Dave, I still say you should call the 800-624-9896 hardware support line (that's NOT the same support number - 888-257-6372 - that's in most of their literature)... if you call the 888 number you would be on hold for a half hour and have to explain the problem a couple times before they'd send you to the hardware number. Anyway, I'm going taking this out of my monitor list, since it's scheduled to be deleted.

My 1/2 cent thought, the 3rd post by Hightechgeek is very technical, it should be kept for reference.
The registry hack or fix could be deleting upper and lower filters and if that is a case that questioner pointed out could be good infor for 39 code error. However, questioner said having no time, then there is no confirm it is how-to solve the problem.

 

I appreciate all the help that came in on my question.  I do feel that no one really gave an answer that was complete and would solve the problem in one step.  Of course I realize that as in many computer problems there is no ONE solution.  I'm going to try all the suggested solutions and feel the registry hack is probably the one that will work.  I'll let you know.
Thanks for the help.

Ok Punky, you get the prize!  Thanks for giving me the leads on the registry hacks.  Your lead was better than the one I had so I thank you for your perserverence.  I'm sorry to say I can't try the suggested fix till next week but will try it and see how it goes.  I think we have exausted all possible fixes, so with them in hand I'll see what I can do.
Again thanks to all who gave help.