Q: iphone 5 turns off randomly, now will not start, will not hard reboot, will not restore in itunes (error 4014) all since latest update

My iphone 5 has started to randomly power down, since last update a few weeks ago.  Last week it would not restart until plugged into a power device, when it restarted with battery still showing over 80% which was where it was when it decided to shut down.  Now it has shut down again and will not restart, and will not respond to a hard reboot (power on and home button together).  It does not respond when plugged into a recharge source.  When connected into itunes it downloads software for a few minutes, then reports that it cannot resotre due to unknown error (4014).