This happened to me before...
This MIGHT work and it worked for me with a broken power button.
Hold down the 'home' button and simultaneously hold the phone firmly on it's top end with the 'power' button depressed against a hard surface for about 10 seconds.
You might feel like you're about to smash your phone, but you must push it firmly against a hard surface (desk/table/cabinet) and it should work.
worked for my iphone 4