A fire on board would cause any responsible pilot to make for any nearby airport and they would be radioing Mayday.
They darn sure wouldn’t fly another four hours and turn off all communications during an emergency.
Pilots are trained to fly first and radio for help whenever they can. 777 are two man crews so if one is fighting a fire the other guy is on oxygen keeping that sucker airborne. Any type of intense fire in the avionics bays will melt wiring. 777 are fly by wire so no control if your wiring is melted together.
I had a bird that had a fire that melted all the autopilot wiring together. Pilot could not disconnect the autopilot system. He pulled the circuit breakers but because the wiring was fused this did not remove power. He could not turn, descend nothing,the only control he had was engine control so he could slow down or speed up. He was able to overpower the autopilots clutches after 15 minutes of fighting the controls.