I may add that by replacing the resistor, you only repaired part of the problem, the wire the shop mentioned may just have a burnt connector.
After you check the fuses you will have to trace the wires back to see, where exactly the wire is no longer making contact, if it is just at the plug it should be a easy fix.
if the wire was somehow burnt along the harness you will need to disconnect the battery and expose the wiring harness back to the source of power.
cutting out any burnt wires and soldering in a new wire or wires depending on the severity.
If you skip this step and have other wires that were burnt along with the power wire for the fan you may have more unpleasant problems show up.
A wires that burnt along the harness can present a real potential for a electrical fire.
If your not comfortable repairing vehicles and wiring it is best to have a professional do this type of work.
Some shops will trace the wire back to the source cutting it out of the harness then run a new wire along side of it, reestablishing the connection yet leaving the unknown alone.
you may get lucky with this type of repair but who knows for sure.
from your description of having a bad wire leaves a lot to the imagination.
if you have to go this route at least expose as much of the wiring in the harness as you can to inspect the wires while the battery is disconnected.
If any other wire was burnt in the harness do not risk bypassing the burnt wire.
either replace the harness that was effected or take the harness out and replace any wires that were effected.
