The pilot reported that before landing he mistakenly positioned the four-position landing gear selector lever to the down-neutral position instead of the full-down position. He further noted that he did not notice the lack of sound and feel of the landing gear extending and the lack of an illuminated green landing gear position light; he also did not visually confirm that the main landing gear had extended. The airplane landed with the gear up, damaging several lower fuselage structural bulkheads and stringers. The pilot stated that the accident could have been prevented if he had used a checklist to ensure that the landing gear had been properly extended. He further noted that the airplane's landing gear unsafe warning horn had been inoperative for some time. A postaccident examination of the landing gear extension/retraction system did not reveal any mechanical malfunctions or failures that would have prevented the landing gear from extending normally.