How did you get into the room? Unless you saved and reloaded while in the room, it shouldn’t have relocked as I remember how it worked (or I guess you used the cannon to get rid of the door but made the mistake of climbing the ladder in the room). If you have skull keys, that is the usual way to unlock them, I believe the ‘Magic Unlock’ spell should work too, if you can cast fifth circle spells and have the reagents.

You don't have to start over either way. Worst case scenario, if you have no way of unlocking it, you can just walk into the fire place and pass until everyone dies.