I had a similar problem, but with my car, with the dead 12v battery, the keyless ignition system went completely nuts...

Not only does the 12V battery run your interior lighting, it also has something to do with the gear-shift lever. Mine would not shift out of Park, but the car thought the car was not in Park, and wouldn't start the car, but wouldn't turn it off, either. It was a real mess.

Finally - after about 30 minutes of a warning signal squeal - the car shut itself down and had to be towed to the dealer. They replaced the 12V battery, re-set the system, didn't charge me a dime, and apologized for the problem.

In possibly-related news, the passenger-side rear light does not switch on. Perhaps it is shorted out? I don't know, but I'm keeping a close watch on this situation.

So far, no further problems.