There is a check valve in the City Water Inlet that prevents water from being pumped OUT that inlet when using the water pump.
Normally a plastic valve with a spring that you can see behind the washer with screen on the City Water Inlet.
It sounds like the Check Valve stem has broken.
Your city water supply will work fine if it is broke, and you can still use the water pump IF you cap off the City Water Inlet. However, it sounds as if the City Water Inlet connect needs to be replaced. I've never seen on that was "repairable" when this happens.
2013 Rockwood 8289WS
Mods: Central Vac, PI EMS-HW50C, 2025RV, (2) SCS225 Trojans, PD9260, Awning Remotes & LED Lights, Eliminators, External Water Filter,, Intellijacks
2008 RAM 3500 Cab&Chassis Hauler Bed, B&W Companion Hitch
All My Modifications are at this link: