iPhone 5 unresponsive and Hard Reset doesn't work

My iPhone 5 gave me the 'sudden death' syndrome. It basically froze. I can't access anything on it. Hard reset didn't work. I had my daughter's picture on the screen and now all I see is one of her eyes on the screen. Connect to iTunes, and it asks me to respond via the phone if I want to back up anything. I am unable to respond via the iPhone so basically I can't access anything on it. I have important information on it that I haven't had a chance to back up.