Patrick, you say you can run the refrigerator on “Gas Mode,” but when you switch it to “Auto Mode” does the indicator lamp illuminate? You may have a blown fuse on the lower circuit board. It’s relatively easy to check if you have a volt, ohm multimeter. It’s possible you may have a problem with any number of the components or wiring within the AC circuitry, but the most common cause is a blown AC fuse on the lower circuit board. But when it’s running on “Auto Mode,” that indicator lamp should also be lit.
Here’s what you can do; Unplug the refrigerator from its receptacle at the rear of the refrigerator, through the lower exterior vent. Gain access to the lower circuit board and carefully remove the cover. Once removed, plug the refrigerator back in, turn it on “Auto Mode” and measure for AC voltage at terminals J5 and J6 on the board itself. If the unit is already cold, you may have to turn the thermostat to a lower temperature setting or wait until it warms a bit. You should also read voltage on terminals J7 and J8 as they lead directly to the AC heating element. If you don’t have voltage at these terminals, check for continuity of the 5-amp AC fuse and the 3-amp DC fuse on the board. Chances are the 3-amp DC fuse is good since the DC lamp works inside the refrigerator, but I’m guessing the 5-amp AC fuse is blown. Worst case scenario is the board itself is faulty.
If indeed you have voltage at terminals J7 and J8, then it’s possible you have a burned out heating element. If that is the case, I’d recommend a pro service tech perform the replacement.