I'm having the exact same problem. Have had my s3 a week, and this started yesterday. Try to unlock the opening screen, get the ripple effect, and...nothing. swipe it about 3 times, and get the "unfortunately........" message, with an OK to click, which i do, and then i can use the phone.
Has Verizon or Samsung addressed this issue? I googled it, and apparently others are having the same problem.