I had this same problem.
First, put the songs you want on a flash drive or some kind of removable media (hard drive, dvd, cd, etc...) then when you go to put it on the other comp, you will need to google for a program that will place them back into your library. for the life of me I cannot remember what it is called, but it has a free version and it will let you do like 3 songs at a time. It can be a slow process, but if you dont want to pay for it, it is your best bet