The picture shows where the relevant parts are placed on the logic board. F1, T1 and T2 are marked green. L1 is mounted on the MagSafe PCB and so not seen on the picture.
After you have figured out which of these parts (L1, F1, T2, T2) are defective you can change them. I recommend to replace both MOSFETs if there is at least one damaged.
After replacing the defective parts you can check the functionality by connecting the battery and the power adapter to the logic board. If everything is fine the LED of the MagSafe connector will light up green and switch to orange if battery will be charged. Be very careful.
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