If I've understood you correctly, and the CD drive in the unit is still capable of accepting, reading and ejecting CDs, then power and data must be getting to the unit somehow. The broken buttons indicate a fault inside the stereo somewhere. Depending on your level of experience in electronics / your willingness to mess with your car, opening up the stereo and resoldering some broken wires might fix it.
Since you say the CD drive still works, it almost certainly isn't a fuse. You never know though, so it's probably worth checking all the small fuses just to be sure.