Turn off the power to the furnace. Write down what color motor wire connects to what terminal on the control board (Red to Heat etc). Next disconnect all motor wires from the control board. Turn on the power to the furnace.
At the thermostst set the FAN to ON. Now go to the control board and look at the connection places where the motor wires connected. Find the terminal on the control board labeled common or C. If you are unsure, you can use the metal frame where you can see metal and not paint. With your multimeter set to volts-AC, CAREFULLY place one probe at the Common or C terminal (or metal furnace frame) and the other meter probe on the COOL terminal at the control board. If you get zero volts, try the Heat terminal. If you get zero volts, stop.
Usually the FAN- ON setting uses the COOL blower speed. So you should have seen 120 volts AC between the COOL terminal on the control board and the Common (C) or metal frame. If you are not seeing any voltages at the terminals, it appears there's a problem with the control board. I would carefully remove it (turn off all power and mark all wire connections). Carefully examine the board for cold solder joints (loose connections) or signs of overheating (burnt area that's brown or black). Also put your nose close to the open end of the motor itself and see if you detect any burnt smell. I doubt you will.