Why does my car smell like sulfur, not start the engine and not turn off?

What is your question?

I have a 2009 mazda 6 (V6 grand touring - push start) with about 60k miles. Had an 06 mazda 6 and never had any issues so I don't even know where to start. It started with the engine not wanting to turn over or taking awhile to do so. Called the dealership and they said no big problem they could get me in next week. As I'm driving home today I start to smell sulfur but thought it was from the construction site I was going through. It doesn't go away and my car still smells like sulfur (rotten eggs) hours later. I try leaving the house a few hours after I got home and my car now won't turn over at all. I try again like the car manual says and now it isn't turning over but I also can't get it to turn off. The engine isn't on but the battery has everything powered, dashboard is all lit up, lights/radio/AC are all on and the push start will not turn the car off. I turned what I could off but still I know it will eventually drain the battery. Honestly don't know anything about cars and take it to the mechanic when a light comes on; so I'm just trying to see if there is a way to get my car started, if it is safe to drive, or if I need to just call AAA to tow it? Any help is greatly appreciated. I have a starter box to jump start it in the morning but I didn't know if you could undo the battery while the car was on. Don't want to blow anything up.