I had another of these iPods, so I opened it up to see what the battery looked like. It had a block connected to it just before the connection to the iPod, which I am taking to be the BMS circuit.
[image|2870646]
So I cut the battery off, just after that block, leaving this:
[image|2870647]
I closed it all up, and plugged it into power, and now just get a cycling Apple logo that shows up for a bit, and then goes away, and on and on. However, I don't get the low battery symbol. I am able to hold down the Home button during one of those power ups to get the iPod to go into DFU mode. However, only when plugged into a wall brick. When the iPod is plugged into a computer, it doesn't appear to get enough power from the USB port to power on at all. Even to just the cycling logo. So I can't try restoring or anything.
It was worth a try though.
Thanks for the suggestion.