Dropped my iPhone 4S, touch screen no longer responsive.

As the title states, I dropped my iPhone 4S (not a very high drop either) which resulted in the screen no longer being responsive to touch.

My home button is broken so I am unable to enter recovery mode/force restart it. I am also unable to do a full system restore because I have to turn off Find My iPhone, which is behind a locked screen which I can't interact with.