From what I can see looking at [guide|56210|this guide|new_window=true], the Magsafe 2 input board is completely passive, it just connects the 5 Magsafe signals to the logic board. It doesn't have any brains to regulate the input power. This leads me to believe that this is a logic board issue and not an issue with the Magsafe board.
Some things that might be worth trying:
* Make sure that the socket on the logic board that the Magsafe board connects to is clean, and no pins are damaged / bent
* Inspect the logic board for damage / burned out components near the Magsafe port