I pretty much went straight from the king to Sir Patrick after the king told me about the dwarven armour. After Sir Patrick asked me if I knew anything about a recent theft on his property, I was able to ask him about the breastplate. Did you talk to the dwarven smith, and maybe talk to the king again? Did you bring him both the axe and letter?
If all else fails, check out
[i]Lost Items -guide and directory of inventory files[/i]. You'll miss out on some experience if you do it this way, and it probably will not help your quest log problem any.