Shorts are quite often capacitors. And hard to pin-point using a DMM, because everything they touch appears as short as well.
Check if the FET measures as diode on some and open on other pins, or indeed it is shorted on some pins
But even if it does appear shorted, while it could be the FET, also suspect any capacitors or diodes linked to it.
Oh, and the nearby transformer also will measure as short, even though perfectly fine.
Barring better equipment like thermal cam, or tricks like seeing where alcohol evaporates first, you may need to desolder stuff and measure them out of circuit.
Always a lot of trouble, as you can do accidental damage while desoldering.