I looked for information on your furnace (I'm assuming it's a furnace) but found nothing. So here's a shot in the dark.
Turn off the power, set the thermostat to cool only, turn on the power and see if the exhaust fan blows. By exhaust fan I am assuming you mean the draft inducer blower for the heating system. If the motor still is runnning check to be sure the furnace is not trying to light. If the furnace is not trying to light I would suspect the control board at the furnace.
With the power off, mark each wire that connects to the control board from the thermostat. Mark carefully because you'll need that to reconnect everything. Now disconnect them all and turn on the power. If the inducer blower runs then I would be more certain it's a control board issue. Have you had any electrical storms recently?