If I remember correctly, you need to do your backup from within I-Tunes. Open the Menus at the top and you will find it. You get options for a Full or Partial backup...it will then tell you how many DVDs you need after it has scanned your collection. Remember to number them as you go.
Once you have created the DVDs, you can "decomission" the old machine(online).
On the new machine you then install the latest version of I-tunes, v 8.1 I think it is. Reboot, defrag and then run your DVD backup,in correct numerical order.
The DRM system stops you from doing it as you have tried, by direct copying.
There is software around that can convert MP4 to MP3. which would allow you to play your music on another type of player, but not an I-Pod. That way at least, you would not have to re rip your CD collection. Hope this is of some help.