I wonder if it's a failed diverter valve (possibly just the motor/actuator). There should be a little lever in the diverter actuator that moves when the motor drives it. This in turn turns on the boiler and pump, I think. You can usually move the lever by hand and slot it into a locking position. That'd suggest a bit more definitely where to start looking.
There should be some stuff on YouTube about checking diverter valves.