I'd guess 0.6 or 0.8 volts would probably be a direct heated cathode for max efficiency. I've seen other odd voltages too, I have little 12" all transistor B&W TV that uses 11 something on the heater for whatever reason, even though the whole set runs on a regulated 12.5 volt supply.
As to OP's problem, the usual procedure needs to be carried out, sketch out a partial schematic (pencil and paper, DMM in continuity mode) as it radiates out from the burnt resistor, then start identifying and testing probable shorted parts (transistors, tantalum caps, etc.), show your work so others can review for anything you may have overlooked. You'll hopefully find the cause near the symptom and not have to reverse engineer the whole board.