I've had that problem with electronics alot on the ship. Resistors don't usually just crap out right off the bat when you change them out, even if they are getting an over voltage. It takes a little bit, (time depends on alot of things including the voltage they are made to handle compared to the voltage that is being slamed through them). Anyway, I would say you have a short somewhere in your system and it's burning up your resistor. As a resistor degrades it takes a higher and higher voltage to get through them...so that may be why your fan only works on high. But you know what man? It could be something as simple as a switch, or a bad connector...who knows? That's the trouble with electronics. Your best bet is to go buy a good multimeter, find a good wiring diagram for that fan, (one that has all your values on it...what your voltages should be, what your resistor should ohm out at, etc) and do some troubleshooting. -OR- forego the purchase of a multimeter and the trouble of finding said tech manual and just buy a new fan! LOL!!! Hell, that's what the Navy would do, (guess that doesn't say much for my troubleshooting abillities does it?)
Good Luck!
-Boze