Hi Dan... It will also not shut down when it's supposed too. Thermostat set at 70 and temp inside is 76! Drop it a degree and then it shuts down.
It's driving me nuts!
Bret,
The gas regulator problem might have explained the problem where it doesn't come on and goes into lockout mode. But it sounds like you've replaced the regulator and still have that symptom.
Both the doesn't start and the doesn't stop could be caused by the thermostat, but if you've replaced it, the next part in line is the relay that the thermostat operates. It's usually located in a box above the Air Conditioner return - if you have Whisper Quiet, it may still be on the underside of the living room AC unit, even if there's no return there.
Could also be a problem with the furnace control board or its wiring having a poor connection, or with the gas valve not opening and closing reliably.
I think I'd check out wire nuts and connections on the control board before replacing parts.