Marty,
Basically - you have a short somewhere on this circuit. make sure that the diode is on the coil first of all. with coil removed - the feed wires arent twisted together are they?? ( i have to ask).
personnally, if it were a shorted transistor, id expect the coil to fire and hold, this then burns out the coil and blows the fuse.
mate - no need to go buying a new board, this will be bloody simple, but these things are only simple once youve found them.
look at the schematics for this coil, follow them through. somewhere along the line, you have a connection that shouldnt be there. trace the wires from the coil right back to the board connectors, any insulation that is worn?? particularly when the looms go round coil brackets, this can wear through the insulation and short 2 wires.
Check the connector with your DMM, anything that has low resistance where it should be high?
ive never got a reliable reading from marvins diode test on transistors, but its probably safe to assume that it isnt this seeing as youve replaced the TIP36 ( it was meant to be a TIP36 yes??).
try having the PF in the upright position also header box open and the lights off. keep an eye on these as you turn the game on - sometimes its best to do this with an extension lead that you plug in while looking at the machine. any blue sparks??? if so - THIS is where your short is.
Check your board for any solder splashes that may be there from previous working.
Somewhere, something is touching that shouldnt be, you just gotta find it!