I have a jet pump with approx. 25'deep with a galv. 1 1/2" dia. suction line, at the top of the line is a tee with the branch end going to the pump, the the top of the tee is a sealed with tephlon tape plug, between the tee branch and the pump is a check valve, I don't know if the bottom of the 1 1/2' galv. suction line has a foot valve,the supply line to the cabin has a 3/4" copper to copper stop (valve)which is turned off, so if the system was working properly the pump's limit switch would shut off the motor after it reached 50 psi, but it doesn't. I have tried a new limit switch, a new expansion tank and a new pump in a process of illimination,I have installed a sedimate faucet at the priming port with a garden hose, when the pump is powered with the sedimate faucet in the off position, the pump pressure is at 19 psi and then I turn the sedimate faucet on, the water comes out of the hose, the pressure drops and the water then trickles out until I turn the sedimate faucet off and the pressure goes back up to 19 psi. When the power to the pump is off after the valve is off the pressure remains 19 psi.

How far down to water?

The water level is approx. 22' that's all I know, cause that's the situation it was when I got to this cabin, so that fact is not for sure...

Your pump will not pump from much more than 25'. If the watertable has dropped much, then that could be your problem. How wide is the bore of your well?

I'm not sure what "The bore of the well is"

How wide is your well? I'm asking because, if I was you, I'd put a submersible pump in.

Well, the well diameter is just approx. 2.5" because the galv. line is 1 1/2" I.D. and the hole it goes in is just a bit bigger. I don't think the water level would be too low either (correct me if I'm wrong) because when I turn the power to the pump off and leave the valves in the off position the pressure stays at 19psi. I don't know... I'm truly running out of Ideas; What if the galv line is corroded with sedimate, I'm guessing if it was a straw and I used tremendous amounts of suction the water would still just come out a bit..?

One more thing, I would just like to say thanks (in capital letters) for the ideas you're passing on to me, I'm not ignoring you, just thinking before I go back to the cabin on the week-end, and making a list of material to bring with me... and try all the ideas you give me...

A submersible pump is a no go. You can certainly try pulling the well pipe and seeing if it's clogged.

With a jet pump, as water level drops, so does pressure. So at 15 feet, for instance, the pump will deliver more pressure than at 20 feet. As depth increases, you reach the point of no return, which in theory is around 32 feet, but in practice is closer to 25. So you could certainly get 19 pounds of pressure, but not be able to get anymore than that. Probably the best thing you can do is make sure you have no leaks in the wellpipe. After that, I'd be out of ideas. Hopefully, someone else on this site can offer some better advice.

Based on a post by another person, and considering that you bought a new pump, make sure you have it wired correctly for the proper voltage. See this post.

https://www.askmehelpdesk.com/plumbing/no-water-getting-pressure-tank-567846.html