The same thing happened to mine, and when plugged into iTunes, it says it needs a system restore. When trying to download, it froze on the progress bar before it started, even when plugged in for several hours.
Try a soft reboot. Hold the power button and Home button down at the same time. Should take about 3-5 seconds and then you will see the "apple". Phone should then take about 2 minutes to reboot. If you don't get an "apple", call Verizon.