Are you stock or rooted? If stock, then talk to Verizon, see if they have any bright ideas. They'll probably suggest you first do a soft reset (i.e., power button + volume down button), and if that doesn't work, do a factory reset. If you've done these things already and tell them so, they might just offer to give you a replacement. It might be a refurbished unit, but a working refurbished unit is better than a faulty new one.
One other thing you might try would be to go to Manage Apps->All->Homescreen, and clear the data. Keep in mind I've never done this, but have read other posts of those who did, who said that it basically wipes your homescreen configuration, leaving you to configure it again manually. Maybe this would clear out some buggy data that somehow got into the app.