iphone 6 shut down with remaining battery. Will not turn on or charge.

iphone 6 shut down with remaining battery one day out of the blue. Will not turn on or charge. I have attempted to do a hard restart with no luck by holding down home and power button for a very very long period of time. Attempted to charge overnight and repeated the above steps, but no luck. Genius bar at the Apple store ran a diagnostic, and informed me that no power is flowing through iphone, so a new one is required. I need to extract data that was not backed up from phone. Thoughts/help?

Is there a way to fix my iphone, or should I just send it off to a specialist that performs pricey data extraction?!?