Pull the panel off the exterior of the trailer, exposing the backside of the fridge. Inside you'll find a metal plate covering the burner section. Remove it and you'll see the gas mechanicals of the fridge. Turn on the switch for the gas function, making sure you have the gas valve open and power available. You should hear a sparking of ignition and a small gas flame should ignite. If nothing happens, some dirt or insects could have contaminated the area and plugged the gas orifice or the thermocouple is misaligned. With the mechanism exposed, it's very easy to determine what isn't working. There is usually a reset switch in the circuit, and sometimes it only takes a poke to have things working again.

The tank also has an electric heater that is used when AC power is selected. With the switch selected to this function, you should be able to feel the heater wrap around the tank for an increase in temperature. If you don't notice a difference, check your breakers for power to the fridge. With a VOM, you can also check the power at the heater which will tell you if it is energised. The electric heater takes longer to warm the tank than the gas, so you may not notice an immediate temperature difference.

Wiring diagrams and trouble shooting manuals are found on the Internet, and can lead you step by step through a diagnosis depending on the make and model fridge you own.

In the same area as Gard mentions, the fridge should have a real plug going into an outlet. Use another item to make sure that outlet is hot.

And depending on the model, most require 12V to run the electronics. So no batt power will do them in too.