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Do you mean something gets burnt in the DCIN board?
Are you using original 60/85W Magsafe 2 charger?
The machine works good with battery, but doesn't start with charger alone?
You've didn't mention F7005 before, which was important.
That means the short is after fuse.
Check diode mode to ground there and be sure Q7180 is not shorted between input/otput pins.
I can only think you don't use original Magsafe 2 charger.
Fake magsafe charger delivers max voltage from the first moment; that could be 15-18V.
Original charger delivers only 3V in the first moment; nominal voltage appears after it correctly detected the board.