jediwarrior,
May the force be with you... No, wait, that won't work. LOL
;p
Seriously, what you need to look for is any startup/automatically running processes/services that have to do with monitoring your optical drive, or else possibly a back-up program. More than likely, you've got something running that is locking up the drive(s). Also another quick way to verify this would be to start Windows in safe mode.
ednachman,
Honestly, the easiest fix without diagnosing your specific issue, I think, would be to create an ISO image of the CD that is problematic on the machine that has no issues with it. Then burn that ISO image to a different brand of CD, assuming it's a burned disk, and try then. If that fixes the issue, then problem solved. You can do the whole thing with one free program called ImgBurn - there are others as well, but that one should do the trick just fine.
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"If to err is human, then I must be some kind of human!" -Me