Are you still using regular lockpicks? If so how many do you have in your inventory?
Talk to Finnigan, do his quest, and you will get an unbreakable lockpick (in a game started in the updated version of the game, you can return the magic lockpick to complete the quest and then buy it back).
What level of the Lockpick skill do you have? The doors require increasingly higher levels to be able to lockpick (the highest needs level 5, IIRC).
However, in this case, it is better to not open all the doors and loose the bet...