Cabin water pump is sending water gushing out fresh water inlet at the post and not thru the cabin faucets. Pump is working but sending water out the inlet.
some folks warn that what I'm about to tell you will break the inlet.> Well. it's broken already so what do you have to lose? (A dry shirt)
Remove the screen washer (Get a new one at the hardware as it likely can stand to be replaced. or reuse it)
There is a little usually white "Button" behind it. With water pump on push button You will get wet IF something is jamming the valve it may flow out. Or not
Connect your water hose to the inlet and turn it on for a minute or so. The check valve is stuck and running water through it, as designed, may close it and knock the debris loose that is holding it open.
Your city water hookup has a check valve inside which allows the water to flow IN and not OUT. That valve is failed, failing and/or is stuck. Whatever the cause, it needs to be replaced so as not to fail again in the very near future. Easy to replace and pretty cheap. Less than $20 buck either from Amazon or Camping World. I've also seen them in the RV section at your local Wally World....Dennis