I've had this happen a couple of times on my 4s. The power/home button solution probably would have worked (should have read this earlier). It's not that the screen is dead but the backlight is turned off. To fix it, I hooked the phone to my PC and iTunes then prompted me to update the phone software. I had to accept the connection on the phone which was a bit tricky without a visible screen but if you touch the screen all over, eventually you will get lucky and accept the connection. As soon as the update starts, the screen will come back on. Let it complete and everything's back to normal.
This should work for the people with broken power buttons.