I have found the solution, switch off your phone for maybe 10 minutes. The RILD problem will persist across phone reboots (hard reboot and even xposed soft reboot).
I had the same problem on S3 and just couldn't figure out why and how to fix until...
You should be able to get a brand new motherboard with warranty claim (hope your binary download count is NO or 0 count)
You may have a faulty charging port (if not battery problem)
Why not download the Galaxy Charging Current app and see if your SIII is charging at 1000mA using wall charger?
Galaxy Charging Current
BTW - Other than faulty charge cable, it could ...
SIII application data folders are here
obb is common used by large HD games like those from gameloft.