Well pump runs constantly; Pressure tank doesn't fill
Allowing for the possibility that it could be otherwise as diagnosis via internet is imperfect....

I see both a pump problem and a check valve problem here. While they may be located in the same place (if your only check valve is on the pump - which is the way mine is set up) they are not the same thing...though I also see another possibility that would do both.


Pump problem - pressure not getting above 27 PSI, or 15 with a faucet open.
Check valve problem - when you shut off the pump the pressure drops
to zero - unless you are using water, the pressure should stay at 27 if it was pumped up to 27. When you only had 10 PSI in the tank, there should have been some water storage - when raised to 38, no water could possibly make it into the tank, since that's designed for 40/60 PSI operation and won't take any water until the the water is over 38 PSI.


The third possibility - you have a leak in the pipe above the pump and check valve - so the pressure is limited, and the water drains away from the leak without the check valve being to blame. If you can go and listen at the top of the well while someone else turns the pump on, you might actually hear this leak, if its in the well above waterline. Or you might have a recently soggy spot in the yard if it's after the pipe leaves the well.

While I don't think it's to blame in this problem, I'd also suggest rechecking your tank pre-charge to see if it has stayed at 38 PSI or started to fall again. Often when the precharge becomes low it's not simply a matter of needing to add air - it's a failure in the bladder or diaphragm.