So I assumed that you been to the mine before in the early days in broken valley and saw the cut scene where the guards blowing out mines, and kill those lower level black ring member outside. Honestly I really didnt encounter the bug myself, so I think you either try using an early save game or via other entrances like kein mentioned. By default, once you climb up the stairs and reach the floor where william is, an auto conversation cut scene will be trigger. You wont need to manually talk to william for the key. IF you really cant get it work, either you had to restart the game or wait for a patch to release to fix the bug.
