Good luck - the same thing happened to me a few months ago with the same symptoms you're describing (dead camera, only the battery icon would show when powered on, everything else unresponsive)
I was told the power circuit is likely bad and would have to be replaced but when the repair shop got the camera the bad power circuit had also caused a short in the main board and that would have to be replaced as well. For the cost I paid for the repair you could probably find a decent used replacement. I just couldn't let me beloved NX1 die so I paid for the repair.