Twenty min after dept, the plt reported that the top latch to the main cabin door opened. An attempt to close the door was unsuccessful. The plt opted to continue the flt. Several min passed when the lower latch opened. The airplane yawed to the rt with a tremendous buffeting. The plt diverted to the nearest arpt. While on an extended downwind to the rwy to reduce alt, the plt reported that the rt engine lost pwr momentarily. The plt could not identify a problem and continued the approach. While on final approach still above the glide slope, the plt reported that an eng quit. The plt could not identify which eng. The plt looked down and scanned the instrument panel to isolate the problem. When he looked back up, the plane was on short final and below the glide slope. The airplane then collided with the terrain short of the rwy. An eng test run was performed on both eng. Both eng were found to run at varying pwr settings for several minutes.