I had a similar problem with a water damaged 15" mid 2009 Unibody Pro.
It would not charge, not recognize the connected power adapter everytime, and would sometimes display a dim green light.
I changed the battery and it still did not remedy the problem
I eventually disconnected the led battery life indicator ribbon from the logic board and it started charging immediately!!
Once I removed the led indicator, it was obvious that it had shorted out due to water damage.
So before trying a new logic board, I would definitely try this!!