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this will require checking the damper motor for power..or seeing if the damper is stuck...do you have a meter? And do you have spring return or powered?
also as a test you could move all zone 1 wires to zone 3 as a test...this would be thermostat wires and damper wires.
If it still does not work you know it is either thermostat or damper.
you can also (as a test) move the damper wires from 2 to 1 just to see if it is damper related. Of course we mark and put everything back where it should be after testing.