So OP Bechard: What did you find out? Did you try turning on the pump when city water was connected? If so what was the result?
I am going with the theory that the pump diaphragm is leaking backwards.
Although I will say every time that has happened to me there has been a little tell-tale water around the pump itself.
I de-winterized this year and had something similar happen but it turned out there was just still a lot of air in the system from the hot water tank and once that was purged it was fine. Took me a while though to figure that.
That was not what happened to you was it? From reading your post I am guessing not.
Those 12 volt pumps are not too expensive, so replacing one is not a barn burner and nice thing is you could put in a new one, tear apart and clean the diaphragm of the original, probably ( better than 50%) that would make the original work again, and then you would always have a back-up. Of course you could send it back to the company (A SHURFLO or FLOJET?) and they would fix it for free (assuming still under warranty) but then you would be out a water pump for the 2 - 3 weeks it took them.
I have lived off the grid for the last 38 years and pressurize my home water system with a DC pump. (Although a 24V version, it is identical) and have come to the conclusion through the years that having a back-up pump available is just the easiest, less stressful way to go. DC pumps just have issues, Sometimes right out of the box, sometimes a couple of years down the road, but issues always come.
Please post what the solution was.
Thanks.