I would concentrate on getting the city water/tank valve fixed first. Many times, that is a three way ball valve that is between the external hose connector, the water tank, and the RV cold water system. In one position, it connects the external hose connector to the water tank, in the other position it connects it to the cold water system. But if putting water into the city water connection causes no flow to either the tank of the cold water system, the ball inside the valve could've moved to, and now be stuck in, an invalid position where it is blocking the hose connection, but connecting the cold water system to the tank fill. In this position, if the pump is running, it could be pumping water from the tank, through the plumbing system, and right back into the tank. The water will follow the path of least resistance (into the tank, in this case) and not have enough pressure to reach any faucets.
The details are probably somewhat different for your coach, but this is a very typical water system for a coach that has a city water/tank fill valve:
Note the control valve in the upper right corner: if it were turned 180 degrees from the "tank fill" position shown, it would completely block off the city water inlet, and let the pump circulate water from the bottom of the tank right back into the tank.
Another possibility is that the flow to the pump is blocked. Usually, there is a clear dome with a filter screen at the inlet to the pump. If you remove this clear cover dome, you should get water flowing out of the tank by gravity. If not, there is often a valve between the pump and the tank, so you can close it and remove this filter screen without getting soaked. Maybe that valve is closed? Maybe the filter screen is so full of gunk it is blocked? The valve I'm speaking of is where the antifreeze adapter connects in the picture above. This might be a three way valve as shown, might be a plain valve if there is no winterization adapter or if the winterization valve is separate.
The water heater may not be filling up because of these issues, or it may have a winterization bypass kit installed, and the valve(s) are set to bypass the heater. Whatever you do, don't turn on the heat until you are sure that the water heater is full. The diagram above shows a single valve hot water heater bypass: typical setups can have one, two, or three valves of various styles.
Putting a cork in the gravity fill, while a good idea for sanitation, probably makes no difference in anything you are reporting. It does not need to be an air tight seal, in fact, there must be a way for air to enter the tank as water is used. If the tank is completely sealed air tight, the pump will be trying to draw a vacuum in the tank as it pumps water: that will either decrease or stop the pump's ability to draw water, or it could cause the walls of the water tank to collapse into the center if the vacuum gets bad enough. There should be an overflow/vent in the tank, as shown above, but the gravity fill can also be a vent (there is sometimes a separate vent tube that is part of it, or there could've been a small hole in the lost cap.
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