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The first thing you may want to try is checking the cabling to the drive.
You will need to disconnect the power to the computer & open up the case. If you have an anti-static band, then wear it, otherwise make sure you discharge your static by touching a metal surface just before you touch anything inside the PC.
Locate the ribbon cable that connects the CDRW drive to the motherboard & make sure that each connecter on that cable is securely attached. Also check the cable for any signs of damage or kinking.
If that all appears to be OK, then you may wish to try testing the CDRW in DOS mode. This will require a boot disk with CDROM drivers on. A windows98 boot disk will do fine. You can download one from here :http://freepctech.co.../files010.shtml
When the system has booted from the floppy, just insert a CD into the drive & see if it can read it.
E.G from the dos prompt (A:>) type :
dir d: (assuming that d is the letter assigned to your CDRW drive)
This should list all the files in the root of the CD.
Another way to do this would be to try & boot from a bootable CD, such as the XP CD.
In both of these cases, you may need to change the boot sequence in the bios to tell the system to boot from floppy or CD before the hard drive.
The only other option which will conclusively test the drive, would be to install it in another computer.