Exposed to rain, cleaned interior, iTunes won't restore

I got caught in a rain/hail storm and my iPod classic got wet. I turned it off immediately and let it dry for a few hours. I plugged it into my computer and it didn't respond, so I put it in a bag of rice for a week. Still no response. I left it plugged into my computer for 24 hours, tried it in a wall plug and in the car, but no response.

I opened the case and cleaned all surfaces with isopropyl alcohol. There was dirt/grit inside, but I didn't see any corrosion (I don't know that I'd be able to recognize it).

I let it dry, put it back together and plugged it into my computer. I hold down the centre button and the Menu button and, after 10 seconds, iTunes says:

Waiting for iPod...

iTunes needs to prepare your iPod for recovery. Please leave your iPod connected.

Preparing iPod for recovery...

But then nothing happens. Other posts indicate that my next step should be to replace the battery. Just want to check that, with my symptoms, this is what I should do. There were visible wrinkles in the foil surrounding the battery when I opened the iPod, but I assumed these were on the protective foil, and not on the battery itself. I'm not sure. The wrinkles were easily flattened with my fingernail. (My battery was silver, not blue like the one pictured in the teardown iPod Classic Teardown). Again, not sure if this was the actual battery or just a foil overtop of it, but I was afraid to tamper with the lithium.