iPod Nano 3G Dead?

I bought a broken iPod Nano 2nd Gen from eBay. Basically it doesn't turn on and I don't see anything on the screen. I took it apart to find a really badly soldered replacement battery that had 0.004v coming out of it.

I removed the battery and plugged in the iPod. I got a USB Device not recognized in XP.

My question is, do you guys think the logic board is shot? If I put in a new battery should the iPod work like normal again? I was thinking that it's not dead since the computer did say "USB Device not recognized" meaning that it did power up somewhat.