dark screen with a light grey or white border

The other day, after I pressed the Home button to exit Siri, my phone started acting odd. The screen went dark and there's white (maybe light gray?) border around the screen. It won't let me exit out of this screen no matter what I do.

I tried restarting, but it just takes me back to this screen. It does connect to my macbook just fine, and my macbook recognizes my device. But I cannot restore or back up my data using iTunes, because I have the 4-digit lock enabled on it, and since I cannot do anything with the screen, I cannot unlock my phone. Please look at the picture below to see what I mean. Does anybody have any clue what the problem is, or how to deal with it?