Do the 3 desktop computers have the same or similar model optical drives, or fairly old ones? That's the only way I would think a conflict might occur with a couple different copies of the same DVD.
Check if there are any firmware updates for the optical drives (ie which may fix a conflict with the copy protection), either with the computer manufacturer's site or the optical drive maker.
Do you have a Linux live CD around? If so, you could try the disk in Linux to help narrow down if the problem is hardware or software (IIRC the Ubuntu live CD loads into memory and then releases the optical drive so it can be used, and other distributions probably do as well). If you don't have a Linux live CD, try booting into Safe Mode (hold F5 down as Windows starts, or F8 to bring up a boot menu, IIRC), which could help eliminate a software conflict or driver problem as the issue.