First I would let the car sit and idle in your yard and make sure your fan isn't kicking on while carefully watching the temperature guage. Assuming the fan doesn't kick on, you would have to troubleshoot to see if the problem was the fan itself or a wire or sensor going to the fan.
I would hook the fan direct to the battery and check it first. Be sure it is properly grounded. If you have a small amperage battery charger that is a slick way to test something like that. Or you may want to just remove the fan and have it tested. If the problem isn't the fan itself you will have to figure out the sensor and wiring tracking. Yes, the fan not working would cause the coolant in your overflow tank to boil.