loss of pressure and pump runs continuously

My pump has been working fine in the past, but today I had low pressure. When I went out to look in the wellhouse, there was a leak in one of the lines from the well. I replaced the piping, and as far as I can tell there are no further leaks. After bleeding the pump, it runs continuously, even after reaching the 40 Psi it typicaly stopped at. The pressure will not go higher, but it still runs, staying at that pressure. I turned on water inside the house, and there was still poor pressure, that gradually got worse in less than ten minutes. The pressure on the pump dropped then, and I had to let it get back up. I turned off the valve that closes all the outgoing lines, thus limiting the water in to staying in the wellhouse pipes, but the pump still ran, and a few minutes later the pressure dropped again, this time forcing me to bleed it again.
I can't figure out what's going on. There are no leaks that I can see, after looking at the pipes and checking under the house, but the pump won't shut off. I also made sure the cut off switches could flip, so them being stuck isn't a problem. Does anyone know what it could be? Thanks

Do you have a bladder type pressure tank? Have you checked if the bladder is shot? Also, check the fittings to the pressure switch - it could be clogged up, keeping the switch from reacting properly. What does the pressure guage indicate? I'm not a pro, and I'm probably leaving out things, and maybe having you check things that don't apply, but it wouldn't hurt to check these anyways - they've been common problems with pump/well systems here.

You also need to re-evaluate the fittings you replaced between the well and the pump. They have to be ABSOLUTELY pristine. Even if there is so much as a pin sized gap in a threaded fitting, or an improperly glued slip fitting that seems to look good, there can be NO air leaks.

The leak can be and usually is too small to be visible or show leaking water. The basic premise here is that your pump would much rather suck air rather than water, but air, unlike water is compressible and it will prevent your pressure tank from filling and triggering the pressure switch. And air can get through the tinyest of leaks even if water can't. Air is 800 times less dense than water so you see why this is possible. I assume that you have checked your pressure tank as was previously suggested.