This has also been posted to the Unofficial Buglist #4 at the link below :

http://www.gamesas.com/index.php?/topic/1297205-unofficial-buglist/


SPOILERS LISTED FOR DETAIL, DO NOT READ IF YOU DON'T WANT TO KNOW THE STORY

Quest Chain - The Companions - Blood's Honor

After Kodlak gives you the quest to venture into Glenmoril Coven to get a Witch's Head (or optionally wipe the witches out completely) you are instructed to return to Kodlak.
Upon doing so I fast-traveled to Whiterun, heading back towards Jorrvaskr, The Silver Hands have finally attacked, Kodlak is dead....ok, so now what, Vilkas approaches me, tells me that Kodlak will be avenged, then walks away, and won't start the next quest (Purity of Revenge).

I follow him inside to see if maybe I need to talk to him to start it, there is no option to do so, just normal chat options. The issue at hand though is the following, NOBODY inside that room is able to be interacted with outside him. They are all busy and stuck in mourning. If i go outside, the two companions that slayed the guards just seem to be on constant guard against the dead bodies that they gloat over saying they will not be an issue anymore. You would expect them at this point to sheathe said weapons, and walk inside, prepare for whatever events are to come. I haven't tried using console commands to bypass the bug, nor am I willing to as I do not want to possibly glitch something else out, or skip content....trying to lose the werewolf I decided to become but can't even with the 1.2 patch.

What I have tried that works, attacking the people inside Jorrvaskr, it takes them away from their constant mourning, now they try to kill me, won't stand down. That is literally the only way I can get them to interact with me, otherwise they just sit over the bodies of the fallen and do nothing.

What I have tried that does not work, talking to everyone multiple times, leaving and going back in, waiting, healing, charming, basically anything that is not considered an attack I have tried.

This quest bug existed pre-patch, and still exists post-patch.

So this bug definitely blows, but I managed to get by it following the advice on UESP.

http://www.uesp.net/wiki/Skyrim:Purity_of_Revenge

I think the problem comes from you having already cleared out Driftshade Refuge. This is what I did to resolve the issue.

1) I dowloaded http://www.skyrimnexus.com/downloads/file.php?id=89. I used the one day version. Make sure the data file gets turned on.

2) Load my Skyrim game and wait one in-game day.

3) Walk up to Vilkas, open the console, and click him.

4) Type in player.setstage c05 0 and hit enter.

5) Close console and speak with Vilkas.

Edited cuz I'm stoopit.

And finally you can remove the respawn mod.

Let me know if this helped

Edit: Just thought of something. Instead of using that mod you could just wait 30 in-game days and then use the console. I know you said you don't want to, but this console command should have no other effect on the game. Without using it you may sol in the way of the Companion's quest for quite some time.

The problem also occurs without having cleared Driftshade Refuge. If you have accepted the Helm of Winterhold quest, you need to finish it first before the Companions questline will move on. The advice from the UESP wiki worked for me, but I had to use the console in order to get the helm without killing the boss. Did anyone manage to do this without resorting to the console?

I am having the same problem; however, I hadn't started the Helm of Winterhold quest. I am going to work through it now to see what happens. My only problem is that I am very leery about using he console or using resurrect. I haven't tried it yet with Skyrim, but in Oblivion I messed up my game BIG time doing all that. I wish that they would come up with a fix. I am going to try and complete the Helm of Winterhold quest and wait the 30 game days for them to respawn and see if that works without me using any messing around with the game. Anyone had any luck? I am so frustrated with it though I am not playing the game today.

I'm having this same glitch. Have no idea if I've entered driftshade, but I know I have done no such "helm of winterhold quest." Anyways, I'm about to try a console command for set time scale to something ridiculous. Pass the 30 days without a mod. I'll report back with news.

Didn't work. Vilkas is still broken :[

I will have a chance to finally boot the game back up tonight after work, will update on if any of the advice given fixes the problem. Thanks for the ideas!

Don't even have the Helm of Winterhold quest in my logs that I can find, guess I get to stay a wolf for a while, ah well. Just not going to go through all the effort of trying to fix something that is supposed to be a wind down thing for me, a game. Hope Bethesda fixes this soon! Guess I must have killed something important early, or done something somewhere. Good thing I have other things I can do while I wait for a fix, no point getting mad at a game this large having issues, if it didn't have them I would be questioning the game more.

Got the same problem, Vilkas wont give next quest. I haven't been to Driftshade Refuge and I haven't done Helm of Winterhold quest.
Been waiting months for a fix for this one.