Non-responding phone s6

Welcome to the forums. Have you already tried to force reboot? To do so, press and hold the Volume down and Power/Lock keys on the device for 10-20 seconds. This performs a simulated battery disconnect.
 
Okay. I followed your instructions step by step and the blue light is still on, plus the phone has not responded. Now what???
 
Did this happen suddenly, after the phone getting wet, being dropped or anything similar? Have you received recently a system update? You could try leaving it charging for a while and see what happens. It's quite difficult for us to be sure what's going on.