Windows XP is lying through its teeth?
Get a bootable disk…this can be a dvd or cd, and try to boot up your computer with this bootable disk in the drive. An operating system disk, like a retail copy of XP, or a Linux distro will do.
Or you can download and burn a bootable disk with another computer. The Ultimate Boot CD would work: http://www.ultimatebootcd.com/
If the drive can read the disk outside of Windows, as the machine boots up, obviously it is in good working condition for that type of disk. Since dvd drives use different lasers for dvds vs cds, it is possible for one part to fail and not the other.
You can also try clicking on the link in my signature that says Microsoft support for optical drives. Follow the instructions at that site.