It actually had nothing to do with the quest "a guild without master". All you need to do is to find william only. Once you located him, he will just pass you the key for the locked mine. The quest "a guild without a master" will auto trigger once you met william, and that just require you protect him to get down stair. Even if you fail him and he die, you still had the key of the locked mine he pass you. You will just miss some exp and reward only if fail to protect him.
