Is this the correct sequence for the system? Thermostat calls for heat. Zone valve opens. Circulates water. Water coming back to boiler becomes cool, burner fires to warm water. Continues to circulate. Thermostat satisfied, all shut down. If by design you have two wires coming from each stat back to the controller, remove each stat one by one at controller and jump it out , to see if the burner will fire once the water needs to be heated. I don't think it's the boiler because it comes on for zone one, so I think it's what Jim Katen said, control wire or a bad controller. You may be able to switch the wires on the controller to work a zone that is not functioning now, this will allow you to have heat in the living area or bedroom tonight. ps: Its my understanding from your post that one zone functions fine. Is this correct?