Water damaged. Replaced battery and screen. Is my logic board bad?

My wife washed my daughter's iPod Nano 6th gen.

We tried the rice trick for about a week, but it didn't help.

It was left to sit for a couple months because I figured it was destroyed. Then someone turned me on to this site.

After seeing some of the teardown instructions, and very helpful tips from people like oldturkey03, I decided to invest some time and money into it to see if it can be repaired.

First of all, you should know that when the ipod was plugged in to the computer, iTunes would recognize the device and I could see everything that was loaded. I was told to "restore" it, so I did. That didn't help.

Next, I tore it down and gave the logic board an alcohol bath. I bought a magnifier and used a small model paintbrush to scrub away any signs of corrosion on the logic board.

Then, I bought a new battery and a solder iron. I removed the battery and soldered the new one on. (It's not a very neat job, so keep that in mind as I move on in my story.)

I reassembled the iPod, but it wouldn't turn on. I reconnected it to the computer, and iTunes still recognized it. I even tranferred a CD from iTunes over to the iPod. Since the screen won't work, I have no idea if the iPod would "play" the music or not.

I purchased a new screen / digitizer combo and installed that. Once again, I reassembled the iPod, but once again, it still won't power on. The screen does not light up, or give me any indication that when I plug it in that it's charging.

I need to know what my next step should be. Do you think that the logic board could be bad? If so, why does iTunes still recognize it as if nothing is wrong and I can load music to it?

Should I just cut my losses and give up, or try to replace the logic board? Is there something else that could be wrong? Would the "sloppy" soldering of the battery cause my issues? Even with a poorly soldered battery, shouldn't it power on when plugged in, or at least light the LCD up a bit?

Pretty soon, I'll have enough invested in it that I could have just purchased a refurbished one. I certainly don't want to spend more than that. However, this has been fun, and a great learning experience.

Thanks for any advice you can give!