Have you purchased your CD-ROM recently, and was it an inexpensive one? The reason I ask is that lower line drives do not always center the disc well.
Otherwise, you may have a problem in the controller or data cable--or the CD-ROM device itself. I'm assuming the controller is onboard, since most are these days, of course, and not on an adapter (expansion) board. If it is on an adapter board, be sure it is seated properly. Then be sure the data cable is connected securely on both ends so that the data flows properly. Also check the controller's configuration--its base address, interrupt line, and DMA channel--to see whether it is conflicting with any other devices.
When encountering this almost same exact problem, an old DOS trick (but you need low level DOS drivers for this) was to run a dir command on the drive letter to which the device was assigned while the device was empty (no disk in it). Upon reporting that it could not read the drive, DOS would provide "abort," "retry," and "fail" options. A known good disk would then be inserted and the "retry" option selected. If DOS could then read it, this was an indication that the device itself was going bad. This, incidentally, worked ONLY in DOS.
The alternative would be to attach a known good CD-ROM to the same cable on the same controller. If the replacement works, you have your answer (and it's likely it will). If it still doesn't, try another cable. If it doesn't yet, you may well have a controller problem, in which case you may have to install an adapter board after all.
I hope I have been of some kind of help.
Butch
"It's what you learn after you know it all that counts"