Do you have all the songs loaded to your iPod and were all your tracks purchased through iTunes?
We have a couple of options to move your music, The first would be to use a piece of free software like iPod PC transfer to copy your songs from your iPod to your PC http://www.download3000.com/download_26608.html
Just make sure you click the correct download link to get the free version.
To do that all you would need to do is load iTunes to the new machine then go aheadand authorize your machine to access yoru iTunes account then close iTunes and download the iPod PC transfer software to the new machine then install it and follow the prompts to simply copy your tracks from the iPod to your iTunes on the new machine.
The second option would be to use an external hard drive or thumbdrive and manually tranasfer your files.
Take a look and let me know which method you prefer.
In that case can you download and install the software from the link I posted to your new machine then can you install and run it and it should walk you through the steps to connect your iPod to your new machine and to transfer your songs.
If you have any issues just let me know