I had the same problem happening to my iPhone 4 (iOS 7) last night. It happened when I was uploading something on Instagram -- didn't drop it or anything. The screen looked exactly like yours. It was totally unresponsive. iTunes can't even detect it when I plugged it in my computer.
Doing a series of soft resets fixed it for me. The phone became functional again after the first soft reset, but the stripes was still there, together with some flickering. I turned it off and back on again and the color was back to normal, but the flickering remained. I decided to turn the phone off for the night. Upon turning it on in the morning, everything was back to normal.
In case you don't know how to do a soft reset, all you have to do is hold down on both the lock/power button and the home button simultaneously for 10 seconds.