The problem appears to be in the internal wiring or control board.

Symptom: If I temporarily connect the red low voltage control wire from the transformer to the green control wire for the fan, a relay clicks on the control board. But the blower does not come on.

I have tried re-seating all five of the blower wire connections to the circuit board but this didn't help.

Does anyone have any suggestions? I'm just a homeowner, not an HVAC specialist. I'm positive the problem is not in the stat or any of the five wires from the stat to the Rheem. Thanks in advance for any thoughts.

Could be a bad relay, or motor. If it is the relay and it is mounted to the circuit board you will be replacing the board more than likely. Start by seeing if you have voltage at the circuit board the check the rest of the system for the proper voltages. There should be a wiring diagram on the back of the furnace door. Note the furnace door has to be installed if the unit has a furnace blower door safety switch.