Is there a light on the front panel flashing? If so, it is a code as to what is wrong. Count the flashes between the pause and let us know.
It could also be the circuit board. Trace the 2 wires back to the board from the heating element. (That is located in the chimney above the flame.) Check the terminals coming off the board. There should be 120 volts there. If you have voltage, and the element is cold to the touch, it is a bad element. The circuit board is not smart enough to know if this is bad, so it could be bad and not beflashing on the panel.
If the element is hot and the refer. does not cool, you have a bad cooling unit. I doubt this is the case since you say it works on gas.
Thanks for your suggestions. I checked for voltage at the terminals on the circuit board and there is nothing. I have power to the circuit board. Both fuses on the circuit board are okay. I assume it is the circuit board that is bad. Your comments please.
In checking the service manual for that model refrigerator there are these suggestions.
Since the 3A fuse is for the 12V power and it must have that to operate on either gas or 120V, that has to be good. The 5A fuse is for the 120V power to the heating element and can be checked by measuring across the two terminals that supply the power to the heater, when 120V is selected and the refrigerator is calling for cooling. To check, turn the temp. to it's lowest setting just before you check for power.
The modular connecters must be properly seated on both the eyebrow board and the control circuit board. Make sure that the 120V power supply is good to the power plug, and at the circuit board. You must have 120v on pins J7 & J8 of the power supply board. If it is not there, but the other things are good, replace the power supply. If it is there check the resistance of the heater (about 40 to 45 ohms) and the resistance from each heater lead to ground (near infinity). If the resistance values are not proper, replace the heating element.