Why won't the Blood on the Ice quest start even though I have killed Nilsine?

I'll save you some time here.

You can't complete it. I did pretty much the same thing -- killed Nilsine, got access to Hjerim with the key from Torva, etc. -- and have never been able to start the quest with that character.

I have reset the Windhelm visit count then returned several times at the right time of day. I have used console commands to start and end the quest, both inside and outside the city. I've tried resetting game days (after 245 days Susanna's body disappears), resurrecting the body, resetting my level and leveling up once, entering Windhelm from every angle and time of day, talked to Viola and Jorleif, and tried it at every stage of the Stormcloaks questline. I've picked up everything, found every journal, tried to investigate every InvestigationTarget. Nothing. It's just bugged.

If someone has found a magical console command, go ahead and share it. But I'll take it from the massive amount of discussion without resolution that no one has.

I hate to be the bearer of bad news. It would be great if someone actually has a solution. But the realistic answer here is "whatever the reasons, you can't overcome them." At least as of version 1.4.

Lockpicking your way into Hjerim works.

After investigating Hjerim, and finding the amulet, talk to a guard.

I talked to the guard outside the palace of kings, so, that definitely works.

Okay, so every time I have gone to Windhelm to start the mission, it has always been Frostfall (Month). And every time I've been able to do it. It may be different for other people, but this is all I have to help.