To do a full test of the transistor you would need to pull it, but if it is shorted, you may be able to just check continuity between the Collector and Emitter (looks like it is pins 2 and 3 from the data sheet). If it is conducting (in either direction) with no input at the base, it is bad. You might also be able to do a basic test without removing it from the board, but by lifting either the collector or emitter (the emitter would be easier, as it is pin 3).
As to why the resistor blows instead of the fuse, the resistor is trying to dissipate about 500 watts (100 volts across 20 ohms) it is rated at 2 watts, so it blows pretty fast. It should be pulling close to 5 amps, so the fuse (4 amp) should blow, but my guess is that as the resistor heats up its resistance increases a little and the resistor blows quickly enough that the fuse doesn't blow. It is also possible that someone put in a larger fuse.
That debugging flowchart is pretty nice. Hopefully it is just one of the transistors. I actually hope that when you examine the board around the transistors, you'll find a solder bridge or piece of metal shorting out one of the transistors.