ITunes and VISTA64 problems

I have I tunes on both the laptop with WindowsXP and on the
newly acquired Desktop, HP Q 8200 with Vista 64.

For the latter I have downloaded the latest recommended
version for Vista64, but even though I can see the imported
and saved ( on an external hard drive) play list I can not
play them. When I click on them on this new Vista 64
empowered Desktop, nothing happens.When I click on
Beethoven folder ( which contains many creations by
composer) I can see nothing in the right panel regarding
the overture, for example.

On the laptop I have exactly the same play list and all
works fine there.

Audio is OK, because when I go to the I-tunes store with
the desktop, I can listen to the songs.

Any solutions????
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Is your desktop authorized via your I tunes account to play the files on
your external hard drive?
The Apple web site will explain how to do this.
It will not explain why because there is no rational explanation.
If you bought music from I tunes that is copy protected you do not own that
music, only the right to play it through I tunes as long as you are
authorized by Apple to do so.
There are ways to get rid of the copy protection, some even authorized by
Apple.
It is not clear which computer the external drive is attached to. Whichever
one it is you have to grant full sharing rights through the OS, something
easier to accomplish on XP than Vista, which is something wholly apart from
Itunes authorization.
What you want to do is possible, just not easy, to accomplish.