Several problems with my Galaxy S3

I have recently started having several problems with my Samsung Galaxy S3.

Problem 1
The power button isn't working. But the strange part is that when I hold down the button as to turn it off, the menu that's supposed to come up doesn't show until about a half an hour later. So it's not the button itself that isn't working, as it will function, but with a long delay.

Problem 2
Whenever I turn off the phone and try to turn it on, it will start to power on but then power off. It will cycle like this until I pull out the battery. The phone will vibrate and the screen will flicker before turning off again. When I replace the battery, it will almost always start the cycling of turning on and off. But those times that it doesn't fail to turn on, it'll turn on without a problem.

Any help with these problems will be greatly appreciated.

— modified on Feb 19, 2016, 6:54:55 PM