Hatmann, can you confirm a couple things for me?
1. What OS are you using?
2. Are all your tracks / iTunes folder on the external drive?
If it's a case of your iTunes folder is simply on the external drive, then I believe it's a simple case of dragging that whole folder across to C:\Documents and Settings\whatevername\My Documents\My Music and over writing the iTunes folder that iTunes created when you installed it on your new computer - Job done.
That's providing you haven't started to create a new library with fresh songs on the new computer, please advise?
I'm currently copying my iTunes folder across to an external HD before deleting it off my desktop to test this for you, give me twenty minutes or so and I'll have an answer for you.