iPhone 5 Unresponsive/Can't Back Up

Hey guys! I have an iPhone 5 32GB Black ATT.

I turned on my phone today only to find that the screen is not responding to my touch inputs at all. I have restarted the phone using the hard reset, but that did nothing. I thought a simple restore would do the trick, but when I go to iTunes to back my data up, it says I need to enter my passcode first, which I cannot do since my screen is not responding!! I really need help, how do I back up my importance files? If anyone knows how to get the screen working too that would be great.

-Eddie