It may have to do with the power button sticking. If you take the battery out and then put it back in, it vibrates and then shows the galaxy symbol but only for a second then turns off for good. No light for when it's plugged in either. If this happens you can no longer use your phone.
BUT! If you like your phone enough and don't want to pay to upgrade it you'll have to take apart and remove the power button. It's not that hard though. The reason that you have to remove the power button is because it is stuck (pushed down) and you can't unstick it and will constantly turn your phone off because it's stuck. Here's a video on youtube that shows you how. You'll just need a tiny screwdriver.
https://www.youtube.com/watch?v=xqPma5ujkLM
You'll have to download an app so that it can turn the screen shop because you won't be able to without the power button.