Not all CD players will run an MP3. Unless it specifically states it in the users manual that it can play .mp3 format, you will need to convert your music to a .wma format (which is read by most players out there). And since .wma does not compress the music data the way .mp3 does, you can only get a few songs on it (700mb worth or about 80 minutes).
Now if your player is supposed to play .mp3, and the discs you're burning are not working, ask a friend to burn a couple of discs for you and test them. If yours do not work and his/hers does, then the problem may be in either your software (burner program) or your hardware (CD burner). If neither work, then the problem lies in your car player.