The MOSFet will set you back a princely $4, including shipping.
The cap will set you back, perhaps, a whole dollar ($1).
The controller - perhaps one more whole dollar ($1).

Replace them all. But only *after* you have checked any and all diodes for open or short conditions.

Strange that these devices do not like surges of any nature, and yet they style themselves as jump-starters. Go figure.

Peter Wieck
Melrose Park, PA