Try connecting the drive to another system and test it. If it still behaves the same way, the part of the drive that reads/writes to CDs is probably damaged and the drive needs to be repaired. There is a separate laser for writing to DVDs and CDs, so it is possible for the drive to only read/write DVDs and not CDs when the laser for CD reading/writing is damaged.
If the drive works fine in the other system, then there is nothing wrong with the hardware. Some kind of driver or program on your system is causing the problems.