My new iPhone randomly just stopped working and will not turn on what should i do?

Try a Reset... press the home and sleep/lock buttons until you see the Apple logo, ignoring the slider. Takes about 5-15 secs of button holding and you won't lose any data or settings.

thanks paul, i just had a similar problem, had to hold it for 30 seconds and the apple sign has come up, my phone was vibrating for over two hours completly unresponsive, now my lap top seems to be comunicating too, oh hello, its back on again...thank you!!!!