Q: Car is not starting and new battery didn't work

I usually handle car maintenance but I am working out of the country right now, so my wife has to do it instead. Our car has never given us any problems. My wife thinks that she left something on in the car one night cause when she came back out, it was dead. She tried to jump start it, but it didn't work. I thought maybe she had it hooked up wrong, so we did a video chat and I walked her through it.

The car did nothing when not hooked up; no lights on the dash, nothing. The dash does not light up when they key is inserted. When she jumped it with her car and let it charge for a while, she could get the instrument panel to light up, but when she tried to crank, it was just a soft clicking sound. When she took the jumper cables off, it went right back to being dead. She took the battery from the car to Auto Zone and they said it was fully charged. So, she picked up a new battery and installed it, and it still didn't work. We did discover that if she hooks up her car positive to positive and negative to negative, she gets nothing. But, if she grounds the negative lead to the engine block she can get the lights and dash to come on.