I've looked throughout the forums and don't see this so I'll add as a glitch:

Played through several quests in Windhelm, including the "Blood on the Ice" quest involving Hjerim (spelling?). Talked to Calixto, chose not to sell him the amulet, then talked to the elf lady (the other person recommended by the steward for info on the murderer). She said I shouldn't confront Wuulfurth about him being the butcher, so naturally thats exactly what I did. He directed me to the "patrol the streets" portion, where I promptly found Calixto in the process of trying to stab somebody, so I killed him. Quest updated, showed as complete. Returned to the steward, collected my reward, everything is happy time... Except now I get no option to purchase Hjerim. I did the shatter-shields amulet of arkay, helped the argonians (amulet of zenithar and another one, the pay increase). I killed the bandits that were praying on the Dark Elf refugees, and I just finished taking the city of Whiterun for the Jarl and got my title of IceVeins... but still no convo topic about buying a house when I talk to the steward, just the "what do you do for the Jarl" and whatever the other standard line is. every so often I get a new bounty mission, but nothing at all concerning becoming Thane or buying property, or even that there was a "bit of unpleasantness, can't move in yet" (the biggest issue i've seen from most people concerning this particular house). I've got Breezehome, but it's a pain fast traveling back and forth across Skyrim just to store some ingots or alchemy ingredients.

I think you have to have taken over another city, not just whiterun. Not sure which it is exactly, maybe Markath. After that the jarl mentions he would like to have you in the city because of your help and the option appears. Carry on the stormcloak questline and check after each city. I have a feeling Markath is the one you need to have captured.

Just got the option to buy a house in windhelm,after doing the falkreath hold i think it was, i think it is when you get the title bonecrusher or something like that.

the blood on the ice quest IS glitched
u cannot buy that house until you finish it
it is not dependent on taking over another city

You have to do both the blood on the ice quest, and then take over a couple of holds. I didn't get the option to buy the house after blood on the ice, but did after some of the civil war quests. For blood on the ice i never killed callixto, but implicated the jarl's mage and the mage was arrested and taken away. Then I did civil war quests and I think it is after Falkreath that the option becomes available. Altogether I think you need blood on the ice, helping the locals and the civil war up to falkreath for stormcloaks, or finished if on the imperial side.

I'll take down Falkreath and see if that does anything for me, Never liked that snotty Jarl down there anyways.

Thanks