MY samsung note 3 faced the same problem. I was using my phone and had 75 % battery on it. I went out for sometime and when i turned on my phone it did not turn on. I was shocked, i thought i’ve drained it to 0%. I went and put it in charge then i power on once. It came and showed it had 100%. I took out the charge seeing it had 100%. but then it turned off. i tried power on but that didn’t work it , i tried this again and again. then i removed the battery kept it aside for 5 minutes put it back and then!! It turned on. it was back in the 75% battery.