Update: Applying external power to the battery terminals seems to have worked For reference, the pinout is as follows, from the left side of the iPod: [- T +] The iPod works now, however it’s slightly picky with cables. I can live with that, so I guess I solved it!
Did you remove AC power and the battery? What can happen if one was not to disconnect the battery or the AC adapter (you have to remove the battery to remove a screw, as far as I know anyway) would be that you would blow the backlight fuse. If you shine a flashlight onto the display, do you see the screen image?
Since there is a possibility of water damage, refrain from using rice. It just gets everywhere in the phone and can make the issue worse. The water isn’t the problem, it’s what is in the water. Rinse the motherboard of the phone with 90% or higher isopropyl alcohol, and all the connectors too.