when i put power to the amp, the red "power" indicator lights. When i
send a turn-on signal, the fuse blows and the "fault" indicator
lights.

I'm pretty sure the resistor is fried, because it is burnt black and
there is marking from smoke on the adjacent components. whether
that's the only thing fried, i don't know. But i can't identify the
resistor because the bands aren't visible anymore.

My idea is to fix the part that looks like it caught fire, then go
from there. I'm already bidding on an identical amp on ebay, if i
win that i'll use that one and look at it for reference to fix this
one as a backup.