I can see songs in I-tunes and IPOD, but cannot play them with VISTA 64

I have 2 computers. One is a laptop and I can play songs there fine with Windows XP Pro.
The new desktop shows also the songs (which I imported from an external hard drive), but when I click on them nothing happens. No error message, no playing of the song. Audio is fine, because in the store I can listen fine to an introduction of a song.
How can I proceed????

Have you authorized your iTunes account on the 2nd computer?

Yes, I have authorized account. When I Clicked to authorize right after your reply, it came back that this and the other computer are already authorized.