Mine did exactly that yesterday. Just couldn't get it to come back on. When i looked carefully, there was a fine crack across the screen. I've no idea how. I ended up buying a new one in the afternoon. They quoted £50 to fix it (which i might still do for daughter), but a new one was £70. I think you'll need to take it to a shop, if removing and replacing the battery doesn't work.
i am getting calls through but screen is blank, cannot answer calls, phone cannot be switched off. i will try what u guys have suggested though how do i remove battery from iphone 4 ?