Okay, when you get your computer restored and connected, download vPod. Yes, it's safe, it's what I used to transfer my songs a while back.

(maybe a year ago)
Then follow the directions the program gives you. (I'm not sure if anything has changed) It won't tell you to plug in your iPod until it's completely installed (or it prompts you to do it). Wait a couple minutes while it transfers, then all of your songs should be in your iTunes.
But make sure you don't plug in your iPod before you download vPod. iTunes will ask if you want to update your library for the new restoration you made. Make sure you click CANCEL if that happens. I did that once and I'll never regret it.