The same thing happened to my iPhone. Since i don't live in the us and the phone is unlocked i cant take it but to an Apple store. If i find out what to do to fix it, ill tell you and you do the same ok.
Take it to the Apple store. They replaced my 3 month old phone. I told them it died on the charger. They plugged it in for a couple minutes and when it still wouldn't do anything they just replaced it.