You have one they don't. I've seen this area fail and if you feel the need, call the machine's maker or Microsoft to make it a warranty issue.
For me, I just use Nero, CDBURNERXP or even iTunes and don't need WMP to function.
Windows XP pro. Media Player (10.00.00.3802) shows No CD or DVD burner has been detected, Press F5 to refresh the Player.
System - Hardware shows devices are working correctly, and I can burn/copy CDs using Nero.
Any ideas guys.