The DC in board could Part of the problem, but really the most important thing is to look all around the logic board for any corrosion. If you find any, look to what it does, does the trace connect to a battery monitoring chip? Does the pin on the chip connect to the DC in board? Look all over, even on the other side of the board, for any corrosion at all. My 2009 MacBook Pro was completely wiped out by a little bit of corrosion smaller than a crumb, so it is definitely possible that the power delivery circuit, which is on the edge of the board, was damaged.