Try re-flashing the stock NC5 firmware using Odin.
I have no idea why this is happening, but logically, I think that would have to work:
- You've already tried clearing the sources of security policies that disable settings (credential cache and device administrators). Also encryption, but you say the device was never encrypted.
- The problem persists after a wipe / factory reset, so it can't be caused by any of your apps or settings.
- I'm 99.999999999999% sure that this cannot possibly be caused by a hardware issue.
- I don't believe in black magic or possession by ghosts or demons.
So there's really nothing else left; whatever the problem is, it pretty much has to be caused by some problem with the firmware. Not only does that seem to be logically necessary, the circumstantial evidence heavily supports this theory: it happened when you upgraded the firmware, without (I infer) making any changes to the configuration or installing any apps.
And since the NC5 firmware isn't supposed to disable these settings, it's probable that either there's something wrong with the firmware you downloaded, or something went wrong with the upgrade process. So re-downloading from a reliable source (I've used the firmware linked above at least a dozen times, and never encountered a problem) and re-flashing should fix it.