I accidentally killed the orphanage lady before I started the quest. She just pissed me off, sadly it will not acknowledge that I have finished the quest and I haven't been contacted. Is there another way to join the Dark Brotherhood?
If you talk to the Aventus Aretino afterwards his reaction is the same, and then after you sleep the Dark Brotherhood comes for you.
I just confirmed this. Ran in and murdered her, I didn't get a bounty even though all the kids watch, and then I went to Windhelm to talk to Aventus and the quest starts and ends all within the first conversation with the boy.
If you haven't talked to Aventus Arentino before, it's perfectly fine. You can just talk to him after and after about two or three text boxes, you get a text box that says you've killed her already. After that, the quest is completed. Then you can carry on and go to sleep (in the game) and the Dark Brotherhood will snatch you up and everything will go just as the same as if you talked to Aventus Arentino before you killed Grelod. Hope this helps.