If you're suspecting the power button....first of all - does the phone react in any way when you connect the charger. If it's the power button, the phone's display should react when the charger is plugged. If the phone does react, your quickest way of getting access to the phone is by opening it up and pressing the power button yourself
You might want to consider watching this too:
https/www.youtube.com/watch?v=4kGsRiEfdWI
The power button that stops working is a common issue son these phones - it might require replacing - but that should only be performed by someone trained - it's not very complicated ut you need solder, soldering gun, a new switch..