I stumbled upon a bug that will not let you continue the Companions quest line and wanted to warn/share. Please keep in mind that this is a guess on my part but I believe the issue was caused by the below information (basically, clearing out the dungeon Driftshade Refuge associated with the quest). I was able to start this quest on another save file that did not have the dungeon associated with it cleared. I started another save file and rushed through to Whiterun to confirm and below are my findings.
Please ensure that before starting the "Purity of Revenge" quest that you haven't previously cleared out the associated dungeon called Driftshade Refuge. If you have cleared it out, please ensure that you wait 30 in-game days to allow the Silver Hand to respawn prior to speaking with Vilkas (turning in the quest Blood's Honor)
If you previously cleared out the Dungeon and start the above mentioned quest, it will not show in your quest log or the map, thus not allowing you to move forward in the quest line.
To Bethesda:
Please see above for possible bug fix. I tried waiting 30 in game days to see if that would resolve this issue however, since I have already spoken to Vilkas and he "gave" me the quest, it didnt help. When I try speaking to Vilkas now, there is no option for the quest, only 2 Handed training and the usual choices of "About the Companions" and "Why did you join". I know you guys are very busy and this is but a drop in the bucket but I think its important to bring to your attention. I so wanted to complete this quest line with my pure melee build and I was very much enjoying the quest line. Thanks so much for your efforts and support!
Dirty Steve
