next time you play the game and want the house in markarth, this is what you do, go straight to the jarl and he sends you on a quest to go kill someone, you come back, he rewards you, then he sends you on a quest to get the shield, you bring it back and he offers you to be able to buy property, thats all you need to do, i've done that twice and its worked both times, the first time i had trouble getting the house even though i did every quest in markarth i thought, but on the misc quests list, i forgot to kill the leader, after i figured out what misc quest it was and killed the leader i was able to buy the house, but you only have to do 2 quests to get the house, and be at level 20 i think, thats it...you have to check your misc quest list and figure out the misc quest you're overlooking. most of the problems people have with getting the house has to do with the fact they don't stay focused on the 2 specific quests you need to do to get the house..doing the other markarth quests has nothing to do with the house, they have to do with becoming thane.
That won't work, because I've already gotten the shield.
When I
Spoiler
escaped Cidna Mine the Jarl met me outside the mine's entrance, where I handed over the shield to him.
Also there are no longer any miscellaneous quests in my journal that relate to Markarth.