Misfire By The Moonlight
RAY: The answer to Part A is, unfortunately, probably not. The reason being that at some point along your journey, your charging system has stopped working, causing you to run solely off the battery.
As the battery weakens, there is less and less juice available to fire the spark plugs, creating a weak spark and causing the engine to run poorly.
This is also why the situation worsened with the headlights on, when the available electricity was divided further between the engine and the car's running systems.
[ Car Talk Puzzler ]