I took mine in to another store today, they tried a bunch of things, nothing worked. They had a refurb at the store ready to give to me, so they waved the $35 fee. So I'm charging it up right now and hoping for the best.
My problem happened immediately after I did a profile and/or PRL update. I know there were tower issues or upgrades happening at the time. I don't know if it makes sense, but I wonder if updating the profile during that tower outage did something to the phone.