Screen acts like it's being touched once turned on

It is a hardware problem, they can't fix it unless they go to everyones house... Take it to Verizon and they'll replace it for free. If you are rooted/rom'd I suggest you flash it back to stock with RSD Lite just to avoid any unwanted arguments.
 
Is it plugged into the charger when it starts sending gibberish? That sounds more like the problem people are getting plugging it in to third party chargers. Plugging it into the chargers freaks it out. If you plug it in with the regular charger it should stop. If it's not plugged in to a third party charger when it's doing it, then you have the defective screen and Verizon will replace it. Just call them.
 
Wipe the screen down so there are NO fingerprints and see if the issue stops. Mine is doing that too and if I clean it then it works until I get a few more prints on it. I took it to the VZW store and they shipped me a refurb but when it came in the mail it was the wrong phone completely so they are sending me another. So in the mean time I took off the screen protector and keep the screen super clean and its marginally usable until the replacement comes.
 
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