When you connect your S3 to its charger, does the LED indicator light show up as red (charging) or green (charged)?
Can you boot your phone up into either its Recovery Mode (simultaneously holding the Volume Up, the Home, and the Power buttons) or its Download Mode (simultaneously holding down the Volume Down, the Home, and the Power buttons)?
If not, try removing the battery and leave it out for several minutes. Then put your S3 back together and try booting it up again.