A CD writer and a DVD writer should be able to co-exist without issues. Windows Media Player 9 should be able to co-exist with Nero without issues.
My CD writers (Yamaha CRW2100S, Lite-On LTR-52246S) and DVD writer (Sony DRX500UL) both use Nero 188.8.131.52. My Yamaha CRW2100S is on an Adaptec AHA-2930U2, Lite-On LTR-52246S is on Secondary IDE Channel as Master, Sony DRX500UL is on either USB 2.0 / Firewire.
Possibly may want to elaborate on your setup, maybe another forum member can advise or may have encountered the issue you are having.