How to fix my unresponsive touchscreen on my iPhone 4S?

My iPhone is running iOS 7.0.2, and the touchscreen has randomly stopped working. I can't turn the phone off or put it into DFU mode either because my power/lock button is broken. And finally I can't restore the device because it tells me I have to turn Find my iPhone off on my phone which I obviously can't do because the touchscreen is completely unresponsive. Anyone know what I can do?

Contacting Apple would be my recommendation.

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