I know that I have to do the kill the giant favor for the jarl of Dawnstar to be able to purchase the land, but I can't get him to ask me to do it. I've destroyed the skull of corruption and went on countless bounty missions, but for some reason it's just not coming up when I talk to him.

You may have to be level 22 and above to get the Jarl to give you the quest to slay the gaints.