From the pictures there is a lot of **** and debris around the flue or heater area. If this were mine I would start by giving this a good cleaning. Start at the top and check the roof vent to make sure it is clean and free of anything that would block air flow. Remove the vent cover and actually look down there with a flashlight.
Remove the covers around the burner area and clean the burner and thermocouple with a brush. There will probably be a pretty good build up around them. Also check the igniter tip. Then blow the area out and power up the fridge and put it on manual to see if the burner lights and stays lit.
Switch over to auto and check that the electric element heats. It will take a while but the flue area should get hot. If these things work then replace the covers and it should get cold in 8 to 24 hours. The freezer floor or rear wall should feel cold in an hour or two.
I know this sounds like a lot to go through but I have had a lot of these fridges and 90% of the problems I have had with them were caused by crud in the burner or flue area and poor ventilation.
Look up the manual for your fridge online. It should help you perform the tasks I mentioned. It sounds like your fridge is trying to work and has worked in the recent past. Cleaning and maintenance should do the trick. -Bill-