I have this HP laptop from 2014 and as of recent, I will completely shut it down and if the AC Adapter remains plugged in about a minute later the laptop starts up again. If I leave the AC out, the laptop remains off. Why does this happen?
There must be some fatigue in the Power board, and it make a short circuit. Or the power button. I would take it apart and clean it and look at the parts in the mean times. i'm sure you can find a youtube video on taking it apart. If you find the part is broken, look it up on ebay, for a replacement.