Is the battery dead?  Try rebooting the phone while it is still plugged into the charger.  Try a spare battery.  If you do not have a spare battery you may be able to find a friend with a GS3 to try their battery or stop by a Verizon store and ask them to test it for you.  If the battery is not the problem and repeated battery pulls do nothing, then it's probably a hardware problem.  Does the phone actually reboot and the only problem is the blank/red screen?  If so can you boot into Safe Mode?