Have you tried extracting the music tracks from the CD using a tool such as audiograbber, then using the wav files it makes on your hard drive to make a music CD? If so, then have you also tried making a cd copy of a music CD? That\'s the two most common ways to make a CD, either burn the files individually or just copy the whole CD.
Also, have you tried the CDs you make in more than one CD player? If not, and you later find that the CDs to play fine in other players, then your CD player is just finicky about CDR media. Try the music CD you burned in the burner itself, that way you can rule out the CD player.