I have no idea why the pump or appliance has/have no off-on switch, but I'll procede and answer the question at hand.
The outlet most lilkely has a problem with dirt or corrosion or else the removal of a plug should be a piece of cake. (There's a chance of some mechanical failure due to aging, but read on.)
Shut off the power to your outlet (close circuit-breaker at the circuit breaker panel). Get an emery cloth or thin flat file and scrape and file off the corrosion and remove the dirt as there's some corrosion or dirt in the socket. Clean out thoroughly.
If that fails, go to Home Depot or home improvement hardware store and replace the outlet. If you are uncomfy replacing, then hire an electrician to replace the outlet.
The power outlet that has broken (safety?) ground should be replaced.