The pipe where the water leaves the sump may be clogged. The pump may be bad... Sump pums have a life span of between 5 - 10 years. I just had to replace mine.. One way to test it is to remove the pump and lower it into a washtub of water and plug it in. If it works, then the problem is the exit piping..

Now a question for you: Is your well pump on the cellar? More than likely the foot valve at the bottom of your well is the problem.

Added to what other are saying, your question is a little vague, no offence.

1. Do you mean, that when no water is being requested, the pump is kicking on and off on it's own?

If this is the case, there are a couple of reason it can be happening, but all relate to the pressure switch. Meaning if the foot valve is stuck open or worn out, the water pressure will drain back into the well causing it to turn on. Or, if you have a pressure tank, it could be going bad. Or the pressure switch on the pump could be going out..

2. If you mean, you turn on the water and the pump cuts in and out, then it could be pressure switch, clogged lift line/foot valve or such.

This is purely speculation, it sounds like the well pump motor is bad and it is tripping the internal thermal cutout circuit breaker inside the motor it's self. You did say well, not sump pump. If it's a sump pump, try disconnecting the float switch piggy back outlet plug and plug the pump directly into the outlet to bypass the float switch to see if the pump runs.

A minute and a half or so is how long it takes that internal frame motor protector to reset.