Reference with the logic board model number and not the model of the MacBook, the number will be 820-3330 for your model and the label is located generally at the bottom right of the board (top-side).
Check boardview and schematics for 820-3330 which you can find on the internet.
On the MagSafe DC Power Jack circuit (also known as one-wire circuit) there is a component that commonly gets blown from the use of knock-off (aftermarket) chargers which is U6900. Replacing the chip will fix the problem if that is the case.
U6900 is north-west of the keyboard connector as seen here:
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