Get some non chlorinated Brake Kleen and shoot it at both ends of the firing pin hole. If you feel comfortable enough to remove the firing pin it would be the better option. The Brake Kleen will dissolve any oily deposits on the pin channel and hopefully allow them to be flushed out. You have 1 VERY nice pistol. After spraying, place a pencil, eraser end in first, into the barrel. Hold the pistol with the barrel pointed up and pull the trigger after cocking the hammer. The pencil should jump noticeably if not be ejected completely from the barrel with a good primer strike.
