Okay, so a little bit of background about Fender amps: they're cheap cheap cheap cheap cheap. The board around the charred part is probably a loss, but it's no big deal really for reasons I'll get to soon. The plug next to the charred part only exists because it enables 100% retarded factory workers to assemble that amp quickly. If you look in the top right corner of the schematic I linked, right next to the revision history list, you'll see a TH1 and XF1, which is the crispy thermistor and the fuse right next to it (respectively) in your first two photos. You have to jump back and forth between the schematic (pg. 7 & 9) and the board layout diagram (pg. 8) to follow the wiring path through the CP# (connector plugs), but the thermistor and fuse are between the AC line input and the power transformer primary just like I suspected. The two parts I mentioned don't need to be mounted on the circuit board at all, and like I said earlier the only reason they were mounted on the board in the first place is so Fender can hire people that don't even know how to solder.
The tl;dr so far: charred board probably doesn't even need to be fixed, the thermistor and fuse can be mounted elsewhere no problem.
None of what I've said so far addresses the actual cause of the fire though, so here goes that. Earlier I thought the burnt part might be a MOV, which is irrelevant because it's not that. Now that I've seen the schematic I can see that it's a NTC thermistor, which is a current limiter when the power is first turned on, and then after the power's been on long enough to warm TH1 up it acts like a short circuit. So without getting too deep into the theory, I'll just say that it's entirely plausible that this one single part just went bad after 30 years of abuse and set itself on fire. I can go into more detail if you want, and the more specific your questions, the better the answers will be.