What I don't understand is why Windows Media Player is unable to play his own media file?
Anyway, I may have another solution for you but this one may seem radical :
Convert your music files into an other format, like the MP3, OGG or m4a.
You can use dBPowerAmp (note that the MP3 codec for dBPA isn't free) or MediaCoder Audio Edition.
For fun, convert one (be sure to keep your original) and try to play it with WMP.