You can redownload iTunes purchases by:
Downloading past purchases from the App Store, iBookstore, and iTunes Store
You can also copry yur iTunes libray from the old computer to the new computer by:
iTunes: Back up your iTunes library by copying to an external hard drive
An iPod can only sync to one iTunes library. If you sync to another library, like you did, the iPod will be erased and its contents replaced with what is in the iTunes library of the second library/computer.