I had the same issue with my Note 3. My phone is always in the waterproof case and never drop bad, but one day, the screen went black. I tried to do everything like removed battery, hold the power button for a minute for so many time, but nothing work. I could just only see the green light when I started the phone, the home and the back button when I pressed the home button. I thought my phone LCD went bad, it would be costly to replace. The next day, I just disassembly my phone (https://www.youtube.com/watch?v=XJlsLUNsvRo) then put it back together. After finished, I tried to turn on again for couple time, and the LCD working again. I just went back and reset my phone and it's still working ok now.