Two issues with Atwood furnaces:
1 - The control board easily gets wet and won't work until it dries out.
2 - The control board goes bad.
Since the A/C and thermostat work then you are getting 12 VDC to the control board - verify the ON/OFF/RESET switch for the furnace is in the ON position.
If you don't even get the fan running when heat is called for it is most likely a control board issue although it could be a fan issue. The furnace will not attempt to light unless it sees the fan is running by the sail switch.
Replacing the control board is a DIY project and I highly recommend you use the aftermarket Dinosaur board instead of the OEM replacement board.
https://www.amazon.com/gp/product/B009XU7H8Q/