Iphone4 won't switch on?

Hi, my iphone4 switched itself of yesterday, whilst I was running and using the phone for nike+ app. It had battery life but has been non-responsive since? I have done all the regular restore procedures, charge for 30 minutes then restart and even tried to restore through itunes, but no luck??

On itunes, it says 'n/a' and doesnt register the usb being plugged in?

Please help, this is driving me mad!!!#

Any suggestion?????