Pump problems
It is very likely a problem with the pump and/or pump motor since the capacitor kick starts the pump motor. First, check the ohms of the wiring going from the pump control box to the wellhead. There are specific guidelines for the wiring resistance readings. You may be able to find the specifications on the lid of the control box. If not, check the website for the specific type pump you have, i.e., Goulds, Meyers, etc.
If the ohms ratings of the submersible wiring is right, you most likely have a pump motor problem. There is one other thing to check. Pull the well cap and drop a plumb bob down to measure the depth of the well and the water level in the casing. The pump should be no closer than 5 feet to the bottom of the well. If it is closer than that, it may be sucking mud or silt and that may have partially plugged the pump inlets, causing a heavier than normal load on the pump motor.
You may have to raise the pump slightly in the casing.