I recently installed a DVD/CD driver and everything runs well for a while but then the computer starts beeping. Any ideas?

The beeping can be just a keyboard key sticking, and that is what is beeping.
Replace it with an old keyboard.
if it keeps beeping you un-install the DVD/CD driver
Try to start your computer without it.
Does it beep again?
Most of CD/DVD are plug and play, but if it was used my be defective.
How you ran Driver detective?
If it is not a keyboard key sticking, you can remove everything but mouse, keyboard,and monitor.Remove evrything else like adapter cards, etc.
I think you may have one of two things, first are you using a Video card or an embedded video port in the motherboard? What I would do, is first disconnect your power supply cable, use a ESD Wrist to discharge electromagnetic electricity, then get a can of Dust cleaner and, remove Ram sticks, clean with dust cleaner Ram slot and also clean Ram stick gold pins with alcohol (perhaps an over kill) and, re-install Ram one stick at the time. Also un-install Video card if you have one, and clean slot and install it right back. Depending on your computer motherboard specs you may start your computer with one stick of Ram. Also try to start your computer in safe mode, I guess by pressing F8. Does it keep beeping?
Is your CPU fan keeps working?
Can you check the CPU temperature?
Can you check Chip Set temperature?
I hope you don't have to get to all the above. 0 Gravity

Yes.
Pay attention to the beeps, these are called "beep codes" They can tell you what the problem is. all you have to do is count the beeps, and are they long, short, both? Go online, type in "Computer Beep Codes" in the search box, and check out the references. Once you have the code matched with the reference, you can start to troubleshoot with a clearer direction.