I assume on the control board there are 2 relays, one for cooling air flow and one for heating air flow. A gremlin is causing the relay (either one) to close. To close the relay requires a signal from the microprocessor. The problem could be a sick microprocessor or other component on the control board or possibly something flaky in your house power to the furnace/air handler.
I would turn off the power to the air handler then check all 120 volt wiring paying close attention to the ground (bare wire) and neutral (white wire, usually) connections. Check the wiring from and at the furnace back to the circuit breaker panel. Double check the house ground at the circuit breaker panel and the neutral/ground bond to the power company neutral/ground. Possibly you have a floating ground.
If the problem still persists, check the control board for cold solder joints. I will try and find details on your specific model and add more later.