Does your fresh water tank have water in it? If so, you could be sucking air on the input side of the pump. Pin holes in the line, leaks at the fittings.
The check valve in the pump may be faulty, but it would not affect the pumps operation. The purpose of the check valve is to prevent the flow of city water into the fresh water tank back thru the pump.
If the pump continues to run, you may have a leak on the discharge side of the pump.
With the city water off and the pump running. Are you getting air thru the faucet?
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