If the battery is dead then it will shut down and not start back up untill the battery is charged.
If it overheated and you tried to start it back up right awayit wouldn't and you would have to wait for it to cool down.
If you overheated and fried the motherboard or cpu then it wouldn't start up.
Without testing and having the laptop in front of me it would be a guess and for an accurate diagnosis you will have to take it to a shop and have it looked at.
The cpu could be fried or the motherboard Plus it could be just the battery gone bad and stopping the laptop from turning on.
When the power on button doesn't turn on the laptop it is definetly a hardware issue and it could be any of those things. I wish I could give you a better anwer but at this time unless there is something else that you can say about the situation it's not enough for me to tell what it could be.
Have you been having any kind of problems prior to it shuting down ?
Lately i had the laptop format, had blue screen threat.
before it went down i was not able to load any programs. Like when i instal programs,
it gets installed, upon restart, the program folder shows empty.
while open that program it say windows doesnt allow permission to access that path.