Just to clarify when you shut the phone the whole phone power's down.
So then you have to hold the power button down to power it back up ?
If so do a factory reset after backing up to see if that helps.
If it does not resolve this then I'd suggest to arrange to let a Samsung Service Centre have hands on with your phone. This may not be the software update with your phone but a hardware issue that has occurred.
If I can be of any further help then please don't hesitate. Take care. 😎