Black screen on my iPhone 4s

My phone's screen went a little funny earlier, it kept on having flickering lines across like there was some interference somewhere. I switched the phone off thinking that would help but when I came to switch it back on I got a grayish screen with the interference lines across and faded black around the edges. Now the screen is completely black but I know it was switched on because it vibrates when I flick the mute on the side. I tried holding the power button and the home button at the same time but nothing happened. I think it just switched the phone off. The phone doesn't connect to iTunes either. Please help.