How do I move my music from the old style iPod to my computer so I can reload the music to a new iPod?

You really should have your iTunes library on your computer and maintain an up to date backup of it. iDevices are not designed or suitable for long-term data storage. See turingtest2's user tip on Recover your iTunes library from your iPod or iOS device for a list of tools and methods (for both Windows and Mac) that can be used to copy media from your iPod to your computer.