If you have 5V power supply, you should be able to check at least if the board does anything. It's a little tricky to suss out the power rails on this board, though. IIRC, it is set up so that the power to the micro is 0V, and the ground is -5V rail. And I think there's also a -12V rail and linear regulator, or maybe I'm remembering wrong. At any rate, the board runs on just the half wave rectified -13ishV DC, so you could also just feed it 12V at the right spot, with a lab PSU with current limiting. If you can figure it out, you can test the micro/display before buying stuff. There are some polar electrolytics on there to guide you around. And there's also a large power resistor dropping some watts on the -13V rail, for reference. Aside from the Renasas micro controller, everything else on the board is easily replaceable. Triac, transistors, diodes, linear regulators, caps, a dual opamp. That's about it.
I'll open mine up and give you some readings in a bit.
*Ok, yeah, the fuse board has an MOV maybe on it? If that burned out, it could be causing the fuses to blow, maybe? I'm not great with AC.
On the secondary, I'm reading 0.54R. (0.5R with an occasional blip to 0.6R).
If the transformer is good but the main board is toasted, I wouldn't throw out it out. The regulation on this transformer is excellent. 88.8V peak to peak output on the secondary, after it's warmed up. Like clockwork. Even under full load of the iron heater, you don't see any significant change to the output. There are a variety of 936 controller pcb you could adapt to this and possibly fit into the enclosure, if not make your own opamp and comparator circuit with analog control.