Usually the fan control also has a limit device built into it. It is possible that the blower motor itself is not working or the fan and limit control is defective. Jump the fan control to see if the blower motor will run or if the thermostat has a fan on-auto setting turn it to on. This way your will know if the blower motor works.
If the blower motor works then you know it is good. Now you will have to test the fan and limit control or replace it since it controls the blower motor. I would also check around the furnace to make sure no other control or thermal disc is causing the problem.
One last item you might try. Many times as controls get old they will loose there setting. Hold the dial and move the fan lever to a cooler temperature. That will cause the blower motor to come on sooner and that might help the situation.
Wow thanks for the quick response. I failed to include that the blower does come on, but only after the burner shuts down (the dial on the fan limit continues to climb after the burner shuts down). The fan limit never reaches the high safety limit, because once the blower comes on, I can see it 'dialing' back down until it hits the low setting 'off'. I will try lowering the 'on' setting as you suggested and look closer for another hidden limit. If I find one I'll assume that I have a problem with the heat exchanger that is letting hot air blow on the limit and shutting down the burner, but I don't expect to since the wiring is simple and I didn't see any wires straying off to a hidden disc... :) will get back to you with what I find.