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If at anytime you are unable to open the lock as outlined above, there are only two other ways to open the lock. If drilling, the object will be to drill to a depth equal to the part of a key that would normally be inserted into a working lock. Once the bulk of the cylinder metal is removed, pry as much remaining metal of the cylinder and pins out so that the mechanism will turn to unlock.
A locksmith or drilling.  The locksmith will do the least (if any) damage but will probably cost the most.  Drilling is inexpensive but is the most damaging.  Drilling too far could render the lock set unserviceable. Choose a drill bit that will remove the metal from the lock cylinder ONLY.  The lock cylinder is the portion of the lock that turns with the key - it is not the handle.  Generally, most home locks can be drilled with a 1/4" drill bit. Remove the lock set and take to a hardware store to obtain repair parts (new lock cylinder and keys).