After being fully charged, if your iPhone still won't turn on try doing a hard reset. Resetting takes place by holding down your "Sleep/Wake" button (top right of your device) and your "Home" button (the circular button on the face of your iPhone) for at least 10 seconds until you see the silver Apple logo appear. Allow your iPhone to restart before doing any more fiddling with it. No data should be lost.
If resetting fails, you can attempt to restore your device by connecting it to your Mac or PC, and clicking the Restore tab via iTunes. Be sure you're using the latest version of iTunes. Your iPhone must boot up in iTunes to perform a restore. Once you see your iPhone icon on the left hand side of iTunes under "Devices", click the summary tab and then select "Restore".
Your iPhone will be restored to the original factory settings, erasing all of your contacts, calendars, photos, music files and other data on the phone. Automatically backed-up information including text messages, notes, call history, contact favorites, sound settings and widget settings, will be restored to your device.
Once you select Restore, iTunes will deliver a prompt asking if you want your settings backed up. Select "back up" just to be sure before restoring your device. Periodically backing up your iPhone is a good choice when connecting to iTunes to prevent future loss of critical content.
Support: Restoring iPhone Apple.com