2000 Honda Civic LX won't start?

Has lights on the dash, I can hear the click of the relay, but won't crank. This happens intermittently. When trying to start, temperature gauge flicks down to negative/cold. After a while of driving (after push-start) temp gauge moves up to hot when accelerating. Mechanic already replaced starter, battery, thermostat, alternator. Checked radiator, coolant. Mechanic suggested to change battery even if it's only 3 months old, but Autozone tested it and measured 12.7 volts, said nothing's wrong with the battery so they rejected warranty claim. If it's the ignition switch, how come there is reaction ( like temp gauge flicking down to C, I hear clicking of relay, and lights dimming) every time I turn the ignition on? Is it really the ignition key or should I replace the PCM. If the previous owner totalled the car, and the airbag actually exploded but didn't report it and just made something to put it back so he can sell the car as if it's never happened, is it possible that there was something that messed up the starting of the engine? Another problem but I'm not sure if it's related: the A/C compressor also acts up intermittently