The pilot reported that during cruise flight he heard a bang and then engine began to run rough. He immediately diverted to a nearby airport and entered the traffic pattern for a precautionary landing. As the airplane turned onto final approach, he saw an ultralight taxiing on the far-end of the runway that would interfere with his landing roll. He decided to perform a go-around and increased engine power. On the second approach, as the airplane was turning onto final approach, the pilot intentionally shut-down the engine by switching off the ignition and fuel selector. The airplane's main landing gear impacted a barbed-wire fence that bordered the approach end of the runway. The right wing leading edge received substantial impact damage. The propeller and engine support structure were damaged, and the main landing gear had collapsed. During a post-accident inspection, compression was noted on cylinder numbers 1, 2, and 3 when the engine crankshaft was rotated. No compression was noted on the number 4 cylinder. The number 4 exhaust valve was fractured and missing approximately 180-degrees of its valve head. The engine had a total time of 1,996.1 hours and had accumulated 537.1 hours since its last overhaul.