When the pilot selected the gear lever to the down position, only the maingear responded. Attempts to lower the nosegear were unsuccessful and the aircraft was landed with the nosegear retracted. After touchdown both propellers were feathered. However, the right propeller did not stop in the horizontal position and as the nose of the aircraft was lowered the propeller dug into the runway. The right engine was torn from the aircraft and the aircraft slewed to the right, damaging the left wing and propeller. Investigation determined that the cause of the nose gear binding, was inadequate lubrication of the nose gear door hinges. This extra resistance resulted in the actuating mechanism coming out of alignment, which caused the gear to jam. After the engines had stopped rotating, there was insufficient time for the pilot to adjust the positions of the propellers prior to the nose of the aircraft dropping onto the runway.