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If the lights work off the battery, it is not a blown fuse. Either the circuit breaker is tripped to the power converter, or the converter is bad.
The breakers are most often located in/under one of the bench seats of the dinette (this is also where the fuses are).
First check for a tripped circuit breaker. If it is OK, use a test light or voltmeter to test for output from the converter. To do this, disconnect the battery. Clip the ground of he test light or the black lead of a voltmeter to the metal part of the box. Probe the cable post with the light or red lead of your voltmeter. If no voltage is present, the converter is bad.
That all depends on the refrigerator - some require 12V to operate, some do not.
The boiler (cylinder) will get hot with 120V if it is turned on. The refrigerator will plug into an outlet and is not hard wired into the camper. If your outlets will work, there is 120 available to the refrigerator.