I just wanted to throw in my $0.02's worth:

When troubleshooting hardware issues, always start Low-Tech (Simple, low cost possibilities) then try the Hi-Tech (complex, costly) possibilities.

In a situation like this, this is what I would do:
1. Does the Drive look functional?
Check the Drive itself to see if it is functioning to physical actions (open/close drive door, the green light in front of the drive comes on), this would confirm the drive has power and is mechanically functional (but would not guarantee that the laser is working fine, there is data communication present between the mobo and the drive or BIOS/Windows can see the drive)
YES--> GOTO Step #3 NO--> GOTO Step#2

2. Shutdown the PC, remove the power cord from the back of the PSU, open the side panel and check to see if the power cable to the drive in question is firmly in place or not. If you can't tell, unplug the power cord then plug it back in. If possible, try another power connector that is known to be working to eliminate the possibility that the power connector is bad. After this, did the drive become functional or not? NO--> Drive is BAD, replace it.
YES--> Does the Drive show up in My computer now? Yes--> case closed!
NO--> GOTO Step#3

3. Make sure to check the Drive's jumper settings, there might be a cinflict with another drive. However, If there had been no relevant drive jumper changes of any kind and no drive was added to the PC, this is not likely to be the case so GOTO Step#4.

4. During Bootup, go in to BIOS Settings and check to see if the Drive in question is listed (detected) by the BIOS. This section is generally at the first screen or under Basic BIOS settings screen where the system drives are listed (Hard, Optical, etc.). Is the drive listed? Yes-->Check to see if My Computer shows the drive, if not it is likely to be the case of the Upper/Lower Filter registry value added by a CD/DVD Burning software which OEM's link gives you the detailed info on how to check and resolve, a very good link indeed!
NO--> GOTO #5

5. Since the Drive has power and opens/closes, yet BIOS doesn't see it, neither will Windows! Check to see if the data (flat ribbon) cable is loose or disconnected. If not sure disconnect and re-connect, if possible replace the cable with a working one. Afterwards, did the drive shows up?
YES--> Case closed.
NO--> Drive is likely to be bad despite being mechanically functional, replace it.

Do you see the logical Low-Tech to Hi-Tech approach? Starting with the easiest to check possibility (checking cable connections), you narrow down the list to the most complex, costly one (replacing the drive). In between, if applicable could be the software related possibilities which you might have to check for (bad/invalid registry key or values, corrupt device drivers, disabled device in Device Manager, system resource conflict between devices, disabled and/or corrupted services, etc.)

I hope I didn't confuse or bore you?

~TL