Chosen Solution
When charging, my Galaxy S4 (T-Mobile) has the grey battery appear (and vibrate), disappear, and repeats that process over and over (Note that the phone is off/is dead). I tried to boot it without the power button, but all that happens is “Samsung Galaxy S4” and then it will show the grey battery thing again.
Try holding the power + volume down + home buttons together until you get the green text with white text screen and if it stays on there without shutting off then you may have a software issue. If it still shuts off on that screen by itself then try replacing the battery. You may need to reflash firmware so here is a guide on doing so: http://updato.com/how-to/how-to-install-… Sometimes it could be a faulty power button as well (spam clicking it sometimes makes the phone able to stay on).
