Are these WMA files that you ripped from a CD on your own, or are they files you purchased from a music service like Zune? If you purchased the WMA file, maybe it's DRM protected, in which case you wouldn't be able to play it on a device after simply copying it over.
Have you tried playing the files using different media players, like Winamp, PowerAmp, or MortPlayer?
Where are you storing the WMA files on your phone? Does your media player even see them?