You can test the resistor with a meter. If you get a reading of infinite, that means there's a break in the resistor, and that will result in the fan getting no juice. So look for "some sort of resistance reading" or infinite. Infinite = broken.
All the resistor does is insert resistances between the battery and the motor to give you different fan speeds. When the fan switch is on high speed there is no resistance inserted in that path. You can duplicate high speed by using a paper clip in place of the resistor.
Also, the switch for the fan motor could be bad, but this is rare compared to the resistor "wearing" out from cycling hot and cold, which brings on the corrosion. The resistors are made with regular steel wire instead of stainless, that's why they fail.
You could run a wire right from the battery to the fan to make sure the fan motor works and it's not the switch.