I am fairly confident this will work, but read the whole post first
You tick erase all nand as well as the usual two options. Then boot into recovery (should give warnings about unmountable /data) and wipe data / factory reset. Then reboot and it should work / odin a stock rom as normal.
If that doesnt work / or instead you get the correct pit file and flash it as well as the rom and have four options ticked: pit, erase all nand + normal two.
If someone gave me their phone with the same symptoms as yours and said: fix it right now that's what I'd do. I'd also warn them I really need to do more research before doing this and using these two options in odin could brick the phone forever.
I hope this gives you lines of inquiry. I found many mixed messages with the erase nand option, most said nothing of merit except don't do it, some said you must wipe data first (which u can't), some said exactly what I've repeated, some say a pit is enough, others had many steps and files ive never heard of to solve the same issue. There is a large thread in the S3 forum about this, even got mentioned on xda proper. My brief cookie crumbs journey did not return any note 2 threads.
Remember one thing, before using odin, double check every detail. Battery, cable being used, files being used (right ones, md5s), right options ticked, computer is in good health, internet is off, Kies is not running. (I'm sure ive missed some)
If you haven't read prepare to be ignored, or worse.