If you are measuring the 5.4 volts DC at the refrigerator incoming 12 Volts DC connection terminal strip, you MAY have a blown 12 volt DC fuse on the fusepanel, and the LED indicator light for the fuse passes the 5.4 volts you are measuring. When in doubt, don't depend on the blown fuse indicators, but put a NEW fuse into the refrigerator fuse position on the fusepanel.
The refrigerator logic board common to both propane and AC operation MUST have a good source of 12 Volts DC to work. If the trouble with the 12 volts supply can't be found, disconnect the incoming red 12 volts supply wire from the refrigerator terminal strip and run a wire to a good 12 volts DC source. There should be a redundant fuse on the circuit board for the incoming 12 volts DC.
BTW, I had a maddening intermittent fuse blowing problem on this refrigerator 12 volt circuit that also runs the rangetop area lights and fan. Eventually I found that the red supply wire to the refrig was stretched tightly around a corner of the refrigerator rear metal base, rubbing the wire insulation away, and causing an intermittent road shake short circuit to the grounded base of the refrigerator and blowing the fuse for that circuit.