Well, I don't know much about thermostats so I would first look for the safety switch, I know that there is often one in another location that controls power to the thermostat. Then to not look incompetent, if that wasn't the issue I would open up the thermostat and see if anything jumped out at me, loose connections, rusted parts, anything that didn't look right. I would check the breaker, and although probably not affecting the thermostat I would check the A\C's reset button. Then if I found nothing I would tell the resident I had to get a tool or something and probable YouTube termostats if someone wasn't available to help. The interviewer asked if there was anything else I would do, I later thought I would check the voltage, I believe the voltage to the termostat is suppose to be 24v. This answer was apparently good though.