I'd be wary of any nonworking iPod you buy off eBay. I recently purchased a (supposedly working) logic board off there and lo and behold! It's giving me all sorts of headaches trying to get it to work with my iPod. The person could easily have cobbled together a bunch of nonworking parts after salvaging a bunch of broken iPods. There could be damage they're not telling you about (from water, dropping, previous amateur attempts at repair).
It sounds like the problem is the battery, but it COULD be the logic board being broken at the place where the battery's cable connects to it.
You can order it, but make sure you can return it and get a refund just in case & check out the internal parts quickly to assess the damage so you return it in time.
ALSO: if it's simply that the battery is dead, the iPod should still turn on when it's plugged into a computer or a USB to outlet converter. If it doesn't, it's not just the battery, in which case I'd be very wary. Replacing a logic board would cut severely into potential profit. Ask for pictures from the seller to verify their words if you haven't already.