With no water on at all my pressure tank kicks on about every three min.runs for twenty sec. then shuts off.

Hi David,
The first thing I would check would be water level in all the toilet tanks on this system. If the level is too high in any one of them you may be getting a very slight amount of water overflowing into your toilet which could cause the pump to kick in as described.
If the water level is clearly below the the top of the overflow tube. If that is not the problem I would then check to see that you have the correct adjustment on the high/low pessure setting screws. It is important that there is sufficent pressure differences between the two or it will behave as described. Another possibility is the air pressure level in your pressure tank. Make sure it has adequate pressure as per manufacturers instructions. Finally if none of the above were the problem I would invest in a LINEAR one way valve (about $25.00) and install that between the pump and your pressure tank.
If your problem is still un-resolved then you do have a leak somewhere and will have to track it down... hot water tank, dish washer, clothes washer....
Good Luck
Alan