Interesting. OK try this.
Turn off the pump power and turn off that red valve. Run a tap in the house. Do you get a decent amount of water out before the flow stops, or very little?
A little would suggest that the valve is on the outlet side of the pump, I would have expected it to pump up the tank and then stop.
Where is the pump getting its water from? A tank or are you pumping from the supply (naughty).
I wonder if there's a bypass valve that's gone dribbly. It very difficult to see from photos, maybe you could try sketching out what you have?