Having a working device and screen is crucial. I would like to assist you in resolving this device screen issue for you.
I appreciate the troubleshooting steps you have completed so far. I would like to take a closer look into your device. What is your Samsung Galaxy S 5 current software version: View Software Version - Samsung Galaxy S 5 | Verizon Wireless? You also mentioned testing the device in "safe mode"; did the problems with the screen continue while the device was powered up in safe mode? Please keep me posted so that I can further assist.
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