It's doubtful that is the problem, but if youcan get inside the case you will see where the flat data cable plugs in. Just remove and reinsert it snugly.
It may be that that CDROM has just died, either from overuse, old age or just bad luck. The symptom is that they cannot read CD's, despite the lights. This is independent of the drive opening and closing, which is mechanical. This is an optical problem.
There are commercial CD cleaners for the drive available (even at WalMart!) I don't know if this would help frankly, but.....