Right, I had this trouble a few months ago when I first had my new laptop.
I downloaded iTunes and logged in/connected my iPad etc. So far so good.
But the only things that appeared in my library are my purchases from the iTunes store, none of my other 800 songs. When I go to sync my iPad, it asks if I want to remove the songs from my iPad and replace them with what's in my library, which is about 15 songs.
Problem is, all my 800 songs are on my other computer's iTunes library. How do I get them onto my new computer's iTunes library without downloading them all again?