I was wondering if anyone else has had this happen:

I was attacked by a Boethia's Cultist and got the book that gave me the quest to seek out Boethia's shrine. I had already discovered it while exploring, so I went there, bringing a companion with me as my friend let me know I needed a sacrifice. I got her up against the 'Pillar of Sacrifice' and killed her with my equipped weapon (my friend told me there was meant to be some sort of special dagger, I hadn't seen or recieved that). I then went into the the dialogue sequence with Boethia, and she proceeded to instruct me to kill the other cultists. The problem was, there were no other cultists, not an NPC to be seen anywhere near the shrine...
So yeah, I was wondering if anyone else had the same problem, in case it helps, I was level 29 when I got attacked by the cultist to begin the quest, and tried going back again at level 30.
Didn't notice this in the patch notes for 1.1 so i hope Bethesda pick up on it and fix it.

How do you initiate boethias quest? I found the shrine but thats it.

Did the house talk to you and tell you to kill the sarfice?

There should be a guard that asks you to go into the house with you. That is what happened with me and it worked
I think you need to go in with that NPC guard or what ever he was.

I had nothing to do with a house, the sacrifice takes place outside by a big shrine of Boethia, you sure you arent thinking of Molag Bal's one?
And I initiated it by being attacked by a Boethia's Cultist outside the shrine of Meridia, who dropped a book that when I read it, gave the quest to find the shrine, but like you I had found it already.

your lucky you got that far, some others and I have been unable to get [ast the sacrificing bit as everytime we sacrifice someone boethiah repeats the same line of dialogue over and over again. The quest is so broken.