We can use a piece of free software like iPod PC transfer to copy your songs from your iPod to your new PC http://www.download3000.com/download_26608.html
Or if your tunes were purchsed through iTunes you can contact iTunes to re download your songs a single time, Basically iTunes understand that things like this can happen and allow you to request a redownload of your purchased items one time. You will need to contact iTunes support by emailing them by filling in this form http://www.apple.com/support/itunes/contact.html?form=download&topic=Downloading%20iTunes%20Store%20Purchases&subtopic=Download%20errors
Once they receive your email they should allow your account a one time download licence for all your content.
Let us know if you need more info or if you would like help trying to move the files.