Chevy Equinox 2005 AWD turns off by itself.

What is your question?

My car was fine until I stopped at the grocery store and when I got out 30 min later it would not turn on. I turned the key and there was no sound of the engine turning and all it seemed like the battery had died. I got the car battery replaced but as I was coming home and standing on the red light the car turned off again on its own. After a while, it can start up again but then it turns off without warning. Also, a notification light that was not there turned on, you can see it in the picture.

What makes this problem better or worse?

when it is idiling or turned off

How long has your 2005 Chevrolet Equinox had this problem?

2 days