If this can help some, my Kenmore refrigerator stopped running too but I discovered that by tapping on the control box inside the fridge, it would start again. Some mentioned in that case we should change the thermostat control unit but that did not make sense to me. I was not taping the control only the outer case and not that hard. So I took the two screws off only to find out I could stop and starts the fridge just by playing with the wires attached to the control. Both connectors were loose. I took needle pliers and squeezed the terminals so the connections are tight again. Voilà!
There's a video on YouTube about changing the thermostat that has the exact same control has mine. I did not took the whole thing apart. Just unscrew the two nuts and tighten the two wires ( in his case, the black and orange wire )
https://youtu.be/ySYu-umiUp0