Hi and Welcome!
at first, you may have a look into the manual of your car stereo if there is a statement about supported media and formats.
The "standard" format is CDDA - CD audio. Any CD burning software is able to make audio CDs from the music files on your computer.
mp3 and wma are compressed audio formats, and the discs are not audio CDs, but data CDs. If you want to play these in your car stereo, these formats must be explicitly supported (again, read the manual), very often there is a logo on the front plate if a device supports wma or mp3. For a 10 years old device, support of compressed audio is very unlikely.
Next point is, that not all players can handle CD-R or even CD-RW since their laser system is not designed to deal with the different reflectivity of writeable media. Another reason might be wear and dust. This Alpine thing seems to have hit the market 10 years ago, so both problem sources - design and aging might apply.
You may have to experiment with different blank media and burn speeds. Also the CD burner does matter in this case.
Cleaning the lens is an additional idea in this case.