music recorded on cdrw disc on computer won't play on cd player?

my daughter has recorded music off the computer onto a cd-rw disc, but her radio-cassette/cd player won't play it. This is the first time she has used a cd-rw disc, previously she used cdr discs which of course can only be used for one recording. Is the problem with the player which is about 5 yrs old, or is it to do with the discs themselves. They will play back on the computer though.
Thanks.
Jim