I would disconnect all power to the boiler and wait 30 minutes then turn power back on. Hopefully that may reset the control board and get the damper solenoid working again.
If that doesn't work you need to verify that the damper itself is free to open and close and also that there is voltage at the damper solenoid when you call for heat. BE CAREFUL. I do not know if that damper is 120 volts AC or 25 volts AC. With a voltmeter measure between the two leads to the solenoid on a 120 volt scale. Even if it's 25 volts, you'll see a needle deflection telling you power is there. If you have power then I would suspect the solenoid. If you don't have power, I'd suspect the control board.
To test the solenoid itself, turn off power to the boiler, disconnect the wires to the solenoid and then measure impedance (continuity) at the solenoid itself. If there is no continuity (open circuit), the solenoid is bad.