The name of the quest (Skyrim)

If you're on PC, you can use the console command unlock to unlock the door. If you're playing on console, you're likely out of luck - reload to an earlier save or live with the broken quest. Alternatively, you may be able to move the save to a PC and fix it there with the console.

All you can do is to load an earlier save game. As you know, there is no console available on the 360, so there is not much choice left.

The other option is to level up your magic skills and do the quest the violent way.