You cant, but I think you should try turning your other computer and logging into your itunes. Then have it on your other computer in your account. Try listening to one song on the other computer and a thing might pop up on your new computer with the songs, it may not work. I have tried it and it worked for me, it doesnt hurt to try!
umm i say copy all your songs to a usb flash drive put the flsh drive in your new coumpter drag all the songs into a music folder(doesnt matter) then drag them all to itunes then they can just convert over then on the advanced tab in itunes authorize your comp your gonna have to enter your apple/email into the bxo and your password hoep i helped you
If you don't have too many songs, a good way to do it would be burn cd's. If you don't want to do that, then I'd suggest you download a program that will transfer music from your iPod to your computer.
http://www.ipod2computer.com/
here is a link to the program I used and it works Great
copy the files from ur other computer into a cd,dvd or usb drive by selecting them all and right click copy thene right click paste on cd or usb drive thene take it to the other computer and copy from usb/cd and paste into the computer.