I have killed the DK's after Samuel left. I found one key they dropped and a key in the gold vase to the West. I have no key that opens the room to the East were the Battlefield 3 key is. Any help as to were I can find this key would be appreciated.

Check the floor closely, and use the alt key to highlight floor items. Two keys will drop from the DK's when you kill them.

I did all this and still no keys. Also, I cannot go to the exit that I can see to the North.

You're not supposed to exit north. You need to go back and use the key you've gotten to leave the citadel. Well, that or blow it up. As for the keys and battlefield key, they should all be in there. If they're not, you're likely experiencing some sort of bug. If it's not on the floor in a place you can't see, that is. Alt should show it if it's there.