The pilot reported that he was maneuvering to land at an airport in mountainous terrain with a field elevation of 8,203 ft mean sea level (msl). As he maneuvered to the east-southeast of the airport over rising terrain, he received a warning from the onboard avionics that he was 500 ft above ground level and two additional warnings for him to “pull up.” The pilot reported that the airplane then began to gain altitude and increase in performance. The pilot then pitched the airplane down and selected full flaps. He reported that his airspeed with in the “150s.” Of note, the maximum airspeed with flaps extended is 117 knots indicated airspeed (KIAS). The pilot continued with the approach and at the runway 1,000 ft mark, the airspeed was 130 knots, then at runway 2,000 ft mark, the airspeed was greater than 100 knots. The landing speed with flaps in the landing position is 85 to 90 KIAS. When the airplane was halfway down the runway (about 2,500 ft remaining) the pilot pressed the go-around button and advanced the throttle halfway for about two seconds before he advanced the throttle full forward. The pilot reported that the engine did not respond, and he checked the mixture and propeller controls and then examined the engine page on his digital display. When he looked outside the cockpit, the airplane had drifted to the right of the runway and continued to drift. The airplane stalled and then landed hard. The pilot reported that he thought he “experienced a wind shear situation” on landing. The airplane sustained substantial damage to the forward fuselage. The pilot did not report that there were any preaccident mechanical malfunctions or failures with the airplane that would have precluded normal operation. The calculated density altitude at the time of the accident was 10,743 ft. The airplane was loaded with 3 passengers for a weight of about 3,250 lbs. The combination of weight and density altitude would have affected the airplane’s ability to climb as expected by the pilot. The recommended visual pattern when arriving from the south involved flying above the midpoint of the runway to the north and make a pattern to land, to avoid overflying high terrain and noise abatement areas. The pilot reported that in the preceding two years, he regularly operated out of airfields around 4,000 ft msl.