IPhone 5s shut off and won't come back on?

My girlfriends phone shut off. And I can't figure out how to turn it back on. She was texting me and it just turned off, while on the charger. She has a back up phone so I found as soon as it happened. But I've tried charging, resetting it on iTunes. And nothing. I don't know what else to try.

You should download the latest ipsw and then restore from itunes by going to your phone and then clicking on shift+restore (if you are on windows) or options + restore (on mac) and let it complete you can download the ipsw here

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