my i phone 4 will not turn on

Try holding both home and power buttons until the Apple boot logo appears.

Try a reset... press the home and sleep (on/off) 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.

If that doesn't work try holding both buttons for about 10 seconds while it's plugged in. I had this happen to me a week ago.