Could there be a sensor on the board that has failed so that it interrupts current to the furnace? A work-round may be to add a switch at the thermostat to send current to the furnace, temporarily. To me, it sounds like a circuit board failure but I have no history with this type of appliance. It may have also been miswired/wrong part installed during the swap.
There are at least a couple of RV techs on this Forum, a couple of them, very knowledgeable about RV air handling. I'm thinking Chris Bryant and douggrainer. I think they hang out in the Tech Issues section of this Forum and that's where you would get the best help, IMO.