Which modem did you flash? Because there's a two fold problem that you're likely facing:
a) you flashed the Sprint modem that is mentioned in the MOAR OP, cuz the rom is a port from Sprint. If you did this, you may have semi-hard bricked your S3.
b) you flashed the Verizon modem, which you aren't supposed to do with a locked bootloader.
Being on the 4.3 OTA, literally the only things you should be concerned with flashing are TouchWiz roms and also kernel modules which enable WiFi.
You're going to need Odin flash VRUCML1 if you cannot access the rom or Safestrap.
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[VZW] Samsung Galaxy SIII