Check and make sure you are burning as "Audio CD" format. Many older players cannot handle CDs burned in MP3 format regardless of type of disc they were burned to while newer car stereos should play CDs burned as MP3s. Additionally, many players cannot handle CD-RW discs. If you have one of those old players you must use CD-R discs.
If neither of the above is your problem, it may just be that the brand of CD-R disk you are using does not work well with your audio player. This happens sometimes and is quite normal. Try a different brand of type.
Another thing to try is to burn at a slower speed. Try burning a disk at 1x (rather than 2x or 6x or whatever speed your burner drive supports). Very often audio CD's burned at slower speeds will work in audio players while disks burned at higher speeds won't. It's been said that the laser encoding is somehow "clearer" when burning at slower speeds and this helps audio players, which often have a problem with home-burned CD's, to cope with the disks.
If your CD won't play at all, this probably isn't your problem but another tip is to try and record all your audio CD's in "disk at once" mode, meaning the whole disk is burned in one pass without turning off the laser. Audio players like disks burned like this better. If you burn the disk "track at a time" the laser is turned off between each track, and audio players often cannot find any track other than the first one on such disks. Although, if you just start them playing at the first track and leave them, they'll usually play all the way through fine.
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