At the very least the TDA7294 chip amp is fried... just going to start there for now.
If TDA7294 would fail, most likely fuses would blow up or something else burn, IC explode. IMO you suspect exactly what survived.
I don't think so. The fuse is a slow-blow 4A, and I unplugged it immediately. It was never left on more than a second. The TDA7294 has its tab tied to the negative supply rail, the tab was screwed to the heatsink, which is what I touched. According to the datasheet of the similar TDA7293, the ESD rating is 1.5kV. I have no doubt the shock exceeded that.
The power LED appears to be tied to the mute or standby pin of the TDA7294, and that LED functions properly still. Even the auto input detection works. So if the signal to the mute or standby pin is correct as I suspect, there should be no way for the speaker to be making noise if the chip is functioning properly.
It's certainly possible that everything else on the negative supply rail was taken out as well, but it's just a starting point. I can whack in a TDA7293 instead which is spec'd a bit better and has some features like clip detection I might be able to make use of somehow.