Damn... well is a hard one to fix since we dont get error messages
So I would have to make sure basic stuff is covered.
A) I asume you DO have sound working, like been able to play mp3's
B) You tried playing music CD's in alternative software like Kaboodle, Noatun, Xine, XMMS, or MPlayer.
C) You checked your mixer has the audio CD imput NOT muted.
D) The audio cable (a thin rounded one, not the ribon) from the CD-ROM is connected to your sound card.
E) You tried playing more than just 'that one' music CD
F) it is a CD-ROM and not a DVD-ROM (this last one, I think need some controlers, not familiar with them honestly).
If all that is covered and still is a no go... well then I have no stinky clue what can be.