Re: Oh Shiiiii.... My amp is not working!
Holy &^%*!!! 6550's in board mounted sockets?!? Shame, shame on you, Lee Jackson.
I assume that burned-up blue wire is coming from the power transformer, and is supplying filament current to the output tubes. 6550 heaters draw 1.6 amps each; 6.4 amps is a substantial amount of current, and it looks like those little knife-edge stab connectors can't take it. The way it works is, the bad connection has trouble passing current, and gets warm. This causes oxidation, making the connection worse, making it get hot. Eventually, the whole thing burns up, at which point the current stops flowing, and it all cools off, only the amp's not working.
It's hard to tell exactly what's what in those pics - can you identify which of the pins is "1" on the tube socket, or mark which way the nub in the tube base is pointing? The 6550 has its heater connected on pins 2 and 7, but we need to know where "1" is first.
I'd say get it to a tech, and tell him you want the heater traces on the PC board cut, and replaced with a traditional twisted pair, daisy chained across the board from socket to socket. Replacing the Molex connector is futile, it will just happen again in the future.
Are those black wires with the pink Sta-Con connectors going to the front panel lights? With some creative soldering and/or use of crimp-on splice connectors, you might be able to back-feed the heater bus through the black wires' connectors - they seem to be able to handle the current better.
Another (certainly easier, perhaps overall better) idea would be to keep using the existing traces on the board to distribute heater current, but solder the burned-up wire directly to the main trace. It actually looks like somebody already did that with the other wire in that pair. It's hard to tell in the photo - does it look like there might have been an additional pole on the end of that connector, which has been removed? That little lump of solder holding the blue wire on the trace at the edge of the board doesn't look original - it wouldn't make sense to use the connector for 8 wires, then solder the ninth wire on. I'll better the connector was originally 9-pole.