Need help SOON (switching computers)

Ok, i don't think this is the right section to put this in but i didn't really know where it should go. I just got a new computer and i want to transfer all my old songs from Limewire (on iTunes) to my new computer but I've tried everything (except saving them all to CDs but that would take forever) and i don't know how to do it. I just downloaded Limewire on my new computer, so now on iTunes two "KellysLimewireTunes" are showing up. One has all my songs from my old computer and one doesn't have any. I can listen to the old Limewire songs on this computer, but i can't move them or do anything with them and they're only available when i'm hooked up to this network, and i need to be able to get them like saved to this computer or something so i'll always have them on here. How do i do this??? I need to know soon because leaving this network soon and i don't want to download them all again. The songs are all on my iPod, but for some reason they wouldn't upload to this computer. Help!!!