I see I have raised many questions by not giving enough information. I installed the well pump sytem so it is my fault that the thing is not working. No installer to blame.
There is a foot valve with a built in check valve on the end of the 1
1/4" line going down into the well, so there is no way to get it on backwards.
The pressure switch is mounted to the side of the shallow well jet pump.
The well has plenty of water in it.
I tried replacing the pressure switch with a new one but I still had the same problem.
Pressure tank is fine. I filled the air bladder to 38 psi prior to starting the 40-60psi pump.
I am able to get the system up to 60psi by holding the pressure switch contacts closed for the first few seconds of cut-in at 40psi, when the contacts are jumping open and closed over and over again.
There is a 1 1/4" line running 75' from the pump to the house exterior wall. The last 10 feet or so of line from the exterior house wall to the pressure tank is 1" line, which is probably my problem. I bet I made the mistake of utilizing some of the interior piping and spiced the pressure tank into too small of pipe, as Sylvan Butler mentioned. I probably should try running the last 10' of line to the pressure tank with 1 1/4" line. The inlet opening into the pressure tank is 1", so I figured it would be ok to spice the pressure tank into a 1" line. Maybe it needs to have 1 1/4" line all the way up to the 1" pressure tank inlet opening. I guess I find out if that is the problem. If not, I'm sure if I moved the pressure tank into the well house with the pump, it would solve my problem. But seeing I live with cold winters, I rather have the tank inside the house.