I couldn't get mp4 files to play either unless I chose to "convert for optimal playback" with Roxio Media Manager via Desktop Manager. No idea why that's the case though. I'm talking about mp4 videos, but who knows, that may work for songs too.
Is it because they are protected? I know the songs that I have bought from iTunes are protected. Mpeg-4 Audio File (Protected) or something like that. You could try to burn those files to a disk and then rip them again. That would remove the DRM.
Older iTunes store purchases with DRM will only play in iTunes and on iPods. Newer purchases from iTunes are now available without DRM. There are several ways to remove DRM including upgrading to iTunes+.