You could have a few different problems being masked by the watchdog error.
The circulation pump not running would not cause the watchdog error by itself.
If the circulation pump is not running, and the flow switch is bad, the heater may turn on without any water going through it. This would cause the hi limit to activate the watchdog error.
To test if the circulation pump is working, you would have to test when the watchdog error is not present. If it is not running, the flow switch is open, and the heater comes on, you would have the scenario I posted above.