How do I back up files off of it?

lomonacodesign, first off you must remember that your iPod Classic has a hard drive. as such, water damage usually ruins that drive. I would suggest that the very first thing you want to do is to clean the iPod. Totally disassemble the iPod using this guide. Clean everything, including cables and connectors with +90% isopropyl alcohol. Make sure it is really clean inside the connectors. Use a soft brush. The trick here is to clean often, not hard. You do not want to knock any components of the board. This includes the hard drive cable ZIF connector. Once all that is clean, replace the battery reassemble and see what you get. Right now you most likely are having either corrosion damage or (hopefully not) a short circuit somewhere. The only other thing that you can do is to get a USB-to-ZIF adapter and see if you can access your hard drive separately from your iPod. You can also try to place it in disk mode and see if your OS can access your files, that way you might get to them to back those up. Hope this helps, good luck.