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First of all to transfer songs that were not purchased from iTunes back to your machine from your iPod you will need to purchase a small software program like iPod to Computer which is a simple program that will let you move all your songs and other files back to your PC,
You can donload the free trial from here and the upgrade to the full version will cost $25.00 http://www.ipod2computer.com/index.php?SRC=6&gclid=CIDvtfKmnKYCFUHu7QodRBW-ag
Then 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.
I've downloaded the software and managed to copy the music to a folder on my computer but can't figure out how to get them into my Itunes library. If you can help me with this I'd be happy to accept your answer and give you positive feedback.
Do you know what folder the music is stored in?
If so can you open iTunes and maximize it so it fills the desktop.
Next can you open the folder that holds all your music and then make the folder view smaller so that it sits partially over the iTunes window.
Once you have done that can you click the music folder then press CTRL+A on the keyboard to select everything and then drag it to the itunes music library and let go
Once you do that the music should all move back to iTunes.
After it has all moved can you then click File then Library and choose organize library and then choose consolidate and let it run.
This will move all your music back to the correct folders.
Once that is done let me know if it all looks correct.