I don't think there is anything wrong with having the pump on while city water is on. The pump shuts itself off at a certain line pressure, so will just shut itself off due to the pressure of the city water line. I'm pretty sure I've done this. You can also pre-pressurize the system with city water if you're careful, I don't have the pressure at this house but when SMB filled my tanks I used the sink several times without ever turning on the pump.
pr, there are two brass bypass valves on the hot water heater they should both be in the same position (opened or closed, meaning in this case "open to the heater tank" "closed to the heater tank". I don't think water would flow if one was open and the other closed. There is a tube connecting them across the heater for when they are closed to the tank, although this system (I don't think) has anything to do with the shower cold side.
On the shower... with water pump on or city water pressure, turn knobs to on (H, C or both) and depress the button on the wand. You should at least hear air and get spurting water shortly thereafter. I don't recall any way to shut the cold off specifically before the shower knob itself.
If none of that works I'd turn the pressure off (open the sink after) and pull the rod from the water heater http://www.sportsmobileforum.com/vie...3&hilit=annode
You should get a few gallons if it was filled, and then with the rod out turn the city water back on and see if water flows out. You can also inspect your rod at this time.