Unless the resistor wire is broken, not just the core it's wrapped around, keep looking. Did you bypass the resistor by connecting both wires to one end of it to see if the engine will start? If not, you really should do that. It won't hurt anything to run the engine long enough to get home with the resistor bypassed. Starters don't just quit and then recover on their own, so bring a replacement starter on your rescue mission. The starter works on very close to "dead short" conditions- - - - -30 seconds of continuous cranking must be followed by 20-30 minutes of cool down to prevent permanent damage.
Jerry