Error 21, won't power on unless plugged in

I was asked to fix an iphone4 that got a little wet. Won't turn on unless plugged into wall or computer. When it's plugged in it shows connect to iTunes. When plugged in I try to restore but it goes through the process then shows error 21. Other times it shows battery icon, lightning bolt and low battery red bar. I have changed battery's and charge ports, still I get the same. I have even switched motherboards with another working iphone4. The affected board still shows same issues in the working frame and the working board works fine in the affected frame. So I've determined that the problem is actually on the motherboard. Can someone please guide me in the right direction on what to check next and how to do it? I'm stuck I think the board is not getting power from the battery, but it does get it when plugged in. I think this because whenever the phone is unplugged from the wall or computer it goes out immediately and won't come back on until its plugged in again. Suggestions please?