Hi, just been through the same thing so hope this helps anyone looking for the answer (I know this is quite an old post).
I helped out a friend with his iPod Nano 3rd gen, it went through his washing machine believe it or not.
Wouldn't power up by battery after it had been dried out (he said he left it in the airing cupboard for days) but would perform like normal when it was in a dock. I tried it under usb power and it turned on but cut out just after booting.
Anyway, I told him that the battery had probably shorted and replaced it for him, bit of a fiddly job, and I need to order a new back panel because of the tabs being misaligned, but it works perfectly now.
The logicboard needed a little cleaning up as it had some deposits on it (IPA and cotton bud very gently) and I put a little bit of glue between the battery connectors to replace the rubbery stuff that you remove before desoldering.
All in it cost £10 (with the back panel) and he was well happy, worth a shot!