Why can't my phone be charged after replacing battery?

I'm not sure if this question is accurate, but I will try to explain.

This phone was bought damaged,it would try to boot only to freeze at the apple screen,and there was no background light. I bought it because I read somewhere that a restore might fix the problems. After plugging it in the computer, the apple came up, and so did the light. After some time on the charge, the light turns on and off, but no progress on the booting. He also gave me a new battery he bought for the iphone, so after replacing the old one the issue remains. I then noticed corrosion on the board, I suspected it because the screen shows sign of water damage. Some around the backlight and some round where the battery is touching the logic board. I removed this with alcohol and a toothbrush. Now the light is stable, but it won't charge from the computer anymore so I can restore it, only from the wall. It's like the phone gets more juice or something, because now the power and home buttons work aswell, they didn't before. And when connected to a wall charger the restore symbol on the phone shows up. As soon as i take it out from the wall charger though, it shuts down. I have tried many different cables, none seem to work.

I love this kind of projects, but this is just weird. Is the logic board faulty?