It is well known that not all CDs will play on all players.
I have quite a few DVDs, as I said, which just refuse to play on my home cinema player but play perfectly well on my "spare" multi region one (dirt cheap as well) and my son's player - a video/DVD combi and my PC.
It's not unknown for me to have to rip the DVD and re-record it (I did this recently with two Disney Singalong DVDs which got a "no disc" when inserted into the player although, as before, the PC had no trouble.
I have a suspicion that many retail CDs and DVDs are now using rather poor quality medium to record on (more profit).
Personally, I have both a CD writer and a DVD writer on my PC so, if all else fails, one of them will read the thing and burn to the other. The result plays on anything (not true, won't play on the washing machine, for instance

).
The other thing to remember is that the readers in PCs are slightly disposable and are not as well-built as, say, an expensive sound system as most people either upgrade them or change the PC and throw them away.
The only way to check is to borrow the same CDs off someone else and see if the problem is there.
Of course, it could just be a badly burned set that you have, it happens - maybe the laser was giving out.
Glad you got it ripped anyway.