Can you transfer songs from your iPod to a computer who's hard drive was erased?

(the first two paragraphs aren't necessary, skip to paragraph 3)

My computer's hard drive recently ran into overdrive and fried itself. The company we sent it to was supposed to save all of our files. Well, they saved all the files under my mom's profile, my dad's profile and my brother's profile... but, everything in my profile has disappeared.

I was the computer administrator and my profile was password protected. Also, all my files were not made available to anybody else. So, either my files are trapped in a profile that doesn't exist or they're gone forever.

Anyways, this means that I have 1000 songs that seem to have disappeared from my computer. They are all on my iPod though and I'm wondering if there is any way to transfer the songs back to the computer. I know it's possible to transfer songs from an old computer to a new computer using the iPod, but that involves having your existing library of music.