It's possible this is not primarily an error in WMP, but somewhere else in Windows or with the hardware. Can you try another program to play cd's? You can get some old Microsoft programs from http://www.threetix.net/articles/0008.html, but you'll be able to find a lot of others also.
If one of those work, you might be happy to use them in the future if you can't get WMP to play CD's. Or you might decide to continue your search for a solution within WMP, of course. That's up to you.
At the moment, it's just meant as a diagnostic aid.
Hope this helps and let us know.