Boby G

My furnace turns off when it reaches the set temperature, but it does not turn on again once the temperature drops. However, once I turn the thermostat to the off and then on position the furnace turns on again untl it reaches the st temperature. I suspected that the thermostat is the culprit, so I changed the thermostat, but that did not resolve the problem. The furnace is equipped with ignition control. Could it be the ignition control? Comments would be appreciated.

My furnace doesn't turn on when fan is on the on position (continuously running), but it works fine when the fan is set on the auto position