The pilot reported that during takeoff the cabin door opened and during the climb and on raising the landing gear, he failed to receive the gear “UP” light. The passenger attempted to close the door while the pilot recycled the landing gear. The pilot reported that gear had likely not retracted based on the airplane’s failure to climb and gain airspeed as it would have, had the gear retracted. The pilot decided to return to the airport and contacted the air traffic control tower to visually assess the gear position. While maneuvering for the air traffic control tower to verify the gear, the pilot continued to cycle the gear up and down receiving no indications of a change in the gear position. The pilot reported the floorboard landing gear position indicator showed “GEAR DOWN” giving him the indication that the landing gear was down. The air traffic controller advised the pilot the gear appeared to be in the down position and cleared the airplane to land. The airplane touched down near the 1,000-foot marker on the runway on the two main wheels. A “split second” later, the right main and nose landing gear collapsed, and the airplane slid off the right side of the runway impacting a runway light with the right wing. The airplane’s right wing sustained substantial damage. A postaccident examination of the landing gear showed the landing gear motor would engage for about 5 seconds and then stop leaving the landing gear in an intermediate position. A subsequent bench test of the landing gear motor resulted in the motor failing to engage or move, indicative of it being inoperative.