Check the pump controller to see if you have a 2 wire or 3 wire pump.
Both types of pumps have a capacitor to energize a start winding in the pump's motor. A 2 wire pump has the capacitor down at the bottom of the well on the pump. A 3 wire pump has the capacitor in the controller hanging on the wall next to your pressure tank. The first thing I would do is test the capacitor. If the capacitor or it's relay is bad, the start winding won't get energized an the pump will hum for a few seconds and shut off over and over again.
Possibility two: a bad wire between the controller and pump that's preventing either the start or run winding from getting electricity.
Possibility three: stalled pump motor from bad bearings, sand, or something keeping the pump from turning.
Someone with a volt/amp/ohm meter who knows what their doing can diagnose this pretty accurately before pulling the pump.