No, DVD burners are compatible with CD's, both for reading and writing. Since the drive plays audio CD's, the laser assembly is working properly (the drive uses different frequency lasers for CD's vs DVD's). The drive may be slightly picky about burned discs, but should still work for them.
Which leaves something wrong with the discs themselves. Lower reflectivity, degraded dye layer, poor initial burn...hard to say from long distance. Try them in a different drive on another computer or use an external drive connected to your laptop via USB.
Optical drives do vary considerably in reading ability, and your drive may simply be be poor about reading marginal discs.