Sump Pump.
I grew up with a sump pump, and I agree that they can have a rotten sense of humor. On ours, the float switch would get stuck, often when the power failed and the pit flooded. Once the power came back on, the pump would sit there with the jammed float switch and one of us would have to don big rubber boots to go and free the stupid thing. On a few pumps, the float would actually fill with water and sink. Try getting a coat hanger and hooking the float to pull it up. Also, some pumps have a piggyback plug where the switch is plugged into the back of the motor plug. If you unplug the switch from the motor plug, the motor will run.
If the motor runs, but it doesn't pump, turn it off, lift it an inch or two to let whatever is clogging the inlet fall off, then start it again.
Good luck,
Dave
PS: Stupid question, but is the breaker and GFCI plug/outlet/breaker on and not tripped?