[whynotthinkwhynot]

You should check all your battery terminal connections. It's likely one is loose, and that will give the symptoms you've described. Most likely it's the negative battery terminal, but it could be either one.

The trans won't shift into N without power, but you can force it into gear by using the emergency parking pin release detailed in the owner's manual. That's how you get a non-starting car to tow. You can use the key to press on a point in the shifter console to release the shifter. That's all cars, but your manual will give the specific location. It's typically hidden by a plastic plug that looks out of place.