It may be that your battery got completely discharge, that's a problem not that common, but it happens, it happened to my daughter's Moto G (2nd Gen) about a month and half ago, and I needed to open the phone and unplug the battery cable from the main board, once you do that it reset the battery and allows the battery charging again.
How can you do the same in the S6/edge? That's a good question as I don't think there is any instructions on this yet, plus, opening your phone will void the warranty, so the best idea for you should be asking for a warranty replacement.
You may also try pressing Power and Vol-down buttons for about 10 seconds and it's suppose to do a soft reset to your phone and allows the reboot, I don't know if it will help in your case but you won't lose anything trying it. Just do it with your phone connected to the charger first, if not, then unplug it and try it again.