The pushbutton is electrically isolated from the actual on/off switch for obvious safety reasons. The mechanical coupling mechanism could be broken as could be the switch itself. It is not intended to be repaired by the homeowner but you could try if you are handy. Before investigating, turn offo the circuit breaker to the pump. Likely that is how you had to turn it off anyway.

If this is beyond you, call a plumber. Unfortunately, there are very few options.