Same exact thing happened to me with one I bought from Verizon online - but luckily after only 14 days of owning it (right at the end of my return window). Took it to a store and they gave up on trying to get it to work. Sadly, it turns out none of the stores in my area stock the 32GB blue version of the phone, so I was to call Verizon's online portion to get a new one shipped. As I had no phone to make such a call, they were going to allow me to use one of their office phones.
Once connected, I was told I would have to ship it in and if they thought I had done any damage to the device that I would be charged the full retail price. Annoying as I'm in a Verizon store to verify such a state already and now I need to worry about damage in shipping - but whatever. Then the lady started having me go through their "you're a dumbass" diagnostics stuff (like taking out the battery). I mentioned I had already done so before as had the employees at the store I am calling from. She then said in the most annoyed and rude voice possible: "Is there some reason you can't do it again?". As silly as it might be, that was the straw that broke the camel's back.
Having to wait for the new phone. Having to worry about something going wrong and therefore being outside my safety period despite being a store currently to verify my device's defect. The locked bootloader, inability to stop the camera sound, annoying wifi notifications, inability to toggle 3G/4G without an external app, the constant browser freezing where I would have to kill/restart the process, etc. The decline of the Verizon network as I no longer get signal where others might not along with them never having added full cell signal coverage to my city's subway network while AT&T and TMobile had. The $100/month price tag. The slight that I was one of the earlier online pre-orders yet watched tons of people who ordered after me get it days sooner. Unlimited 4G LTE can only offset so much... I will truly miss the amazing speed.
So - I told the lady on the phone "Um, that's alright, I changed my mind. Thank you." and then hung up. I got back into the queue for a representative in the store and paid $35 for the privilege of returning a defective device (restocking fee). Plus as I had my trusty Thunderbolt with me, I could have them re-activate that there so that I would have a phone again, rather than the difficulty that would have come from attempting it online as my 4G sim card for the phone had to be replaced. Switching to a Galaxy Nexus on Tmobile's $30/month unlimited internet/text with 100 voice minutes that actually arrives today.
TLDR: I've had it happen as well so it seems like it isn't just a fluke. While quite advanced, it seems like these phones may have a slightly higher than average defect rate possibly. No fix that I could figure out for this issue.