First of all make sure you are not burning onto CD-RW discs. These do not work in any audio equipment except for computers.
You have to burn onto CD-R's. It doesn't matter what brand or how expensive the discs are, they all should play MP3 files. This is a big misconception people have. They think the more expensive the CD-R the better quality. This is a joke.
Anyway, maybe it is your CD writer or it could be the speed at which you write it to the CD. Try a slower speed.
Other than that it must be your CD player in your car. A few can't read MP3 files.