First things first: the furnace is designed to wait 30 minutes after a failed start before it will try again. So, unplug your r-pod, disconnect one of the battery terminals, go grab a coffee and wait. Then, connect the battery again (don't bother with shore power, it just complicates things).
Check that the furnace fuse is intact (use a multimeter to be sure). Replace if necessary. The appropriate amperage for your trailer will be written beside the fuse slot.
Also, at this early point in diagnosis, the status of the propane tank and lines doesn't matter. Regardless if the tank is connected or not, a working furnace will cycle and the fan will come on. If there is no ignition, it will shut down after a few minutes of blowing cold air.
As furpod mentioned above - have you checked the settings on your thermostat? Are you sure that its set to heat? Are you sure that the fan is set to auto? Are you sure that the temperature is set well above the ambient temperature?
If everything looks good so far, then your problem is likely the furnace motherboard itself, the wiring or the thermostat. Eliminating the thermostat is easy enough - remove the unit from the wall carefully and then jump the two furnace wires (don't get them confused with the A/C wires); the furnace should start right away. But, frankly, these types of problems are rarely with the thermostat. Checking the wiring is also easy enough - a visual inspection and a few checks with a multimeter. If nothing pans out, your problem is likely the motherboard and its time for a trip to the dealership.