WMP should be able to play that file. So should all other media players. What exactly is WMP doing? Is it giving you an error message, or is it just not playing? Will WMP play other mp3's? Do what Jones suggested and test it with other files. If it won't play them, maybe the codices are messed up, or the program is just broken. Try updating or reinstalling the program.
Have you tried any other media players like Winamp or Musicmatch? If they'll play the files, then the problem is probably WMP. If Quicktime is the only program that will play the files, then there is something queer about them.
Try iTunes. Anything that is compatible with Quicktime is compatible with iTunes, and it might give you more information about the file. It should also be able to convert files into other formats. If nothing else, you could burn the files to CD and then rip them again.