Initially, using the reset procedure for the defrost timer seemed to work (shut off for few minutes, and turn back on), so we replaced the defrost timer board. Also replaced the starting relay and capacitor on general principles. This did not fix the issue (still would not start at all). Talked to a very helpful agent at appliancepartspros.com, and we were able to trace the issue to the thermostat switch (explaining why moving the thermostat control to off and back on sometimes fixed the issue). Shorting the switch resulted in the refrigerator running normally (though continuously). Have now ordered a replacement thermostat switch, which we are confident will fix the issue. The agent was patient and very helpful! Hardest part of the project was getting the control panel bezel off to get at the defrost timer board and thermostat.