Similar problems here: screen blacked, then refused to charge, would attempt to start but then the screen faded to black.
I followed the above instructions - restart button plus volume up - I got a green android icon with, what appeared to be its guts open (!!!). Selected 'factory reset' and it then went through a process of about 5 minutes of reconfiguration. I lost some photos and needed to reinstall some apps.
I think this was a good outcome, and an easy DIY fix.
Still love my Samsung!