The Hungry Deserter

After you reach Ostagar and start exploring, go near the Infirmary and you should see some suspended cages.In one of them is a hungry prisoner arrested for trying to desert.

Background
Quest states: "Help the hungry prisoner The prisoner at the king's camp has begged you for some food.According to him, the guard may have some to give."

Walkthrough
To complete the quest just speak to the guard, he will give you some food.Return to the prisoner and he'll now give you the key. Keep in mind tough that in order to open the chest it needs to be nighttime.

Result
Use the key on the chest near the Magic Encampment to get your reward.