copy & Paste to Docs
Go to the Music heading on ITunes, and when all your music comes up, Hit CTRL+A and then copy and paste the entire library into a folder in Documents. After you have done that, save the folder to a disc or flash drive, but it would have to be a large flash drive. Then use the device or disc that you used to save the music in the new computer and transfer the folder to your new computer. Open the folder and hit CTRL+A again and copy and paste to ITunes that is on your new computer. This should work. If the flash drive or disc isn't large enough for all your music, then you may have to do this in increments until all your music is reloaded. As you add new music to ITunes, copy and paste it to the folder you created for your music in Documents so that when you get another computer in the future, you will have it ready to transfer to ITunes again.