I know that the Companions Quest glitch involving "Purity" has been reported. Most of the topics read the same. I have not found a post yet that is similar to my own problem. After the main quests for the Companions are over and everyone returns from the Tomb to Jorvaskar, they never offer me the chance to do the Purity Quest.
Farkas does not offer me any jobs whatsoever and Vilkas will continuously send me out on his three different radiant quests. So I tried doing some radiant quests for Aela and after having nearly 50 (no exaggeration) Animal Exterminations, Rescue, Recover the Heirloom, etc., in my journal as completed the option to start the Purity Quest is still no longer there.
Being as it might be a "butterfly" effect kind of glitch, I grit my teeth and started over. Completely uninstalled Skyrim as well as Steam, created an entirely new partition on my computer with its own OS (Windows 7 btw), and started the game anew. I figured try to do the quests a bit different than before.
So my first Radiant Quest was from Farkas and then of course when I returned Skjor wanted to see me. Afterwards I did the second Radiant quest also from Farkas and repeated with Skjor. I did Aela's quests after because no one else would offer me a job, her revenge quests if you would. Then Kodlak's final quest. Now I am right back where the glitch began the first time. No offer to even start a "Purity" quests even after doing more radiant quests for Vilkas and Aela. Has anyone else ran into this issue and if so has anyone found a fix? (and no console commands for the quest do not work. They have to give you the quest before you can setstage. I'm not getting the quest to even begin).
Also I would like to state that there are no mods, alterations to the ini., or any other form of outside influence on my game. It is entirely vanilla from the ground up with only the steam and 1.3 updates. Nothing else has been altered. I have not even used console commands to as much as save my game just in case.
Thanks much Community!!

yeah, same problem. No option for curing them.

Did you wipe out the Glen Moril witches or just kill the one to finish the quest? I have never seen the Purity quests either, and just assumed it was because I wiped out the witches (and lost or dumped the extra heads somewhere).

I've played through the quest line several times as well, and never did get the Purity quests. The thing that usually bugs my playthrough, however, is getting caught stealing and then getting the forced greeting "Looks like you've been taking things that don't belong to you" which I can never clear. That always forces a reload/restart for me.

I did completely wipe out the Glenmoril Witches when I went through it. A few other topics on UESP suggested having one of the heads with you when you talk to Vilkas or Farkas, but that did not help either. I would reload an earlier save, but seeing as how it seems Skyrim also has bleeding saves (unconfirmed, just feels that way) I doubt reloading would help. Might try another run through without killing them all. (I have no clue why it turned italic.. Oo)