Power inverter - what component blew
The melted component is a fuse, so it's likely that it has done what it's meant to do and blown before anything expensive fails. It should just pull up with pliers, but it looks like it has melted to its neighbor, so might need some effort separating. It likely has 1/4" blades that are pushed into receptacles on the board underneath. The fusible element itself is in the middle of the body, under the "40" designation, which is its current rating in amps.