Photo #1, near bottom: Black insulation looks ragged where it rubs on thin metal. Bare wire is exposed. Can you verify where is contact and where is continuity? And where it should not make contact?
Your chief problem appears to be removing the ailing mosfet from that cramped compartment. It burned a hole in itself (or it was a tiny explosion?). Is a heat sink underneath it? Is that in good shape?
But is that the only burned component? Is it lodged in a socket connector of some kind? Any further repair should involve testing burned components.