How do I recover previously purchased music? it only shows that I've purchased it, but not how to download it to my new devices.

I have a new classic ipod (the old one died), and I am trying to recover the >5000 songs I had on my previous one (not all backed up, unfortunately). When I go to the store and select certain artists, I see that I have already purchased the music, but when I go into my library, only partial albums show up. Why is this? And how do I get the rest?