Pump pressure issues

Facts: low pressure 20 psi. We had water logged
pressure tank. Changed tank. Water has not gone
into tank. Still only 20 psi. Did not install check
valve. We have a submersible pump. If I turn off
power to pump pressure holds at 20. If I leave
power on but close the shut off valve after guage,
pressure stays at 20. Do you have any ideas?
Should I have put in a check valve? Thanks

A checkvalve won't help. Do you know if there are any checkvalves between the pump and the tank besides the one on the pump? If there are any, they could mask a leak.

Make sure the gauge is good!

Ok so I think I might have a leak between my well pump and house. At the well house I have 2 faucets, 1 on either side of what I think is a check valve. In my basement I have a shut off. My pump runs continually at 20 psi. How can I test to see if there is a leak?

As long as the gauge is good, when the pump is off, if the pressure just stays at 20, you don't have a leak. At least you don't have a leak on this side of the check valve. Sometimes you can have a leak in the little nipple between the pump and the check valve. That leak you won't see until you pull the pump.