This may not be a fatal problem. There are several things that can cause the furnace not to light. First problem is to make sure your batters are good and full of water. If need be take the battery down to auto parts store and have it tested. Even thought you may be plugged in to shore power a bad battery will cause the converter to over work and may not be putting out the optimal voltage.
Another problem could be caused by the trash can. What may have happened is dust and lint has been sucked in to the furnace and has built up on the blower wheel witch will cause the air flow to diminish. There is a "sail switch" in the air flow path that is there to "Prove" that there is air flow and allow the burner to light. If the blower has a lot of build up on it, it will not force enough air to trip the sensor. In this case depending on the type of furnace you will have to pull the furnace and clean the blower.
There are other things that can cause the furnace to not light from low lp pressure to a faulty high limit switch to a bad control board. It may not be that costly of a repair. If you feel that you can do the work your self, I can help you through it with a service manual and guidance here. I would need you to gain access to the furnace and tell me the model number so I can get you the proper information.
Most RV service centers will also test the furnace and give you an estimate for repairs at a reasonable cost and even wave the estimate fee if you accept the repairs, but you would have to take the coach to them or remove the furnace and take it to them.
If you would like help in trying to repair it for you self, Just let me know and I would be glad to help you.
Yes the propane could be the problem. How dose the cook top burner look when light? It should be a nice blue flame, no yellowing or fluttering. If it is a propane issue then you might have problems with you water heater as well when it runs on propane. Do you hear the spark ingitor on the furnace trying to light when it turns on? If you do hear the ingitor sparking "TICKING" then the problem is not the sail switch, I you be most likely a propane issue. You may have to go out side the coach and listen for the ticking and have some one turn on the heat while you are listening. I will take about 60 to 190 seconds after the fan comes on befor the burner will try to light. See if you can hear the furnace ticking and if the cook top has a good flame. If you have access to manometer, witch is a lp pressure tested, you can check for proper lp pressure from the regulator. Depending on the regulator you have, they range from $30.00 to $90.00 and can be perched at most RV service center.
The pressure of the lp should be around 11 inches of water column. Here is what a manometer looks like and it reads in inches of water column.
Locate your lp alarm detector, it is normally located close to the floor on a wall. Dose it have an on/off switch? If you had a power drop some times the lp detector that have the on/off switch will lock off the propane and keep it from flowing. If it dose have the on/off switch just turn it off and back on to reset it. If you do not have the on./off switch then you do not have the lp lock out system.
How are your battery? Have you check the water level in the battery? If you have a bad battery it will cause the voltage to drop. Furnaces need above 11.0 volts of battery power to operated. Even if you are plugged in to shore power, a bad battery can cause the furnace and refer to fail. Have you tried the cook top to see what the flame looks like?