Here's the procedure. See what you still have to do:
1) Get iTunes music onto an external drive
2) On new laptop install iTunes and get it running with no music in library.
3) Click edit->preferences in iTunes, and then advanced tab. There will be a location of where the library is stored -- by default it's something like C:\documents and settings\[username]\my documents\my music\itunes\itunes music. Change this to wherever you want the library. If you're happy with it in the default location, just leave it as is.
4) Drag folder containing all your music from external drive into iTunes window -- wait a while as music is added.
5) Click advanced -> consolidate library, to put all this music in your library location I mentioned in step 3.
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If you like, you can first copy music folder from external drive to your desktop, then drag that folder into iTunes. (I can't remember if pressing consolidate library moves music to library folder or just copies it. Copies I think.)