The reason it's not playing is due the the fundamental differences between CD-ROM drives, such as in a laptop, and conventional CD players in car stereos etc.
CD-R and CD-RW discs use very different methods to represent data compared to normal audio CDs. Low quality CD-R discs (asda, tesco etc) make the problem worse, as does recording the CD at a high speed. The 'bits' which get recorded onto the disc are so small that older CD hardware can have trouble reading it, especially further out on the disc (where the later tracks are located).
Try writing the music on to a good quality CD-R (Sony, etc) and at a low speed, 8x maximum. The CD player should have no problem reading this.
Hope this helps.