I'm having all the same issues that everyone on this forum is having. It's been 2 days and after reading many forums, troubleshooting with the manufacturing website and cell service carrier, and going to the Verizon store (where they said the phone was dead, which I believe they just wanted me to buy a new phone so they get their commission), I gave it one last shot with a suggestion from an S3 forum.
1. Remove battery.
2. Hold power button for a minute to drain any left over battery.
3. Bang/hit phone up against the table with gentle force (yes I know .. an oxymoron) several times. I just banged it up against the heel of my hand. I didn't want to cause any cosmetic damage to my phone.
4. Reinsert battery.
5. Power up.
This procedure sounded weird to me, but I was desperate to try anything. I didn't want to have to shell out money for a new phone. It's been a day, and everything is working fine.
It's worth a shot trying this method. If it helps, AWESOME! If it doesn't, I'm sorry and good luck in trying to find a remedy other than just buying a new phone.