Check the fan switch on thermostat, I've seen this happen so many times. (Just like "tomh said".)
If that is not the case I would say the pc board probably has a heat fan relay in it and the points in this relay are burnt. If you tap the furnace when it's blowing cool air the fan relay may stop the fan.
You will then need to replace the pc board or the fan heat relay whatever the case. You'll need a furnace repairman for this operation.