On May 15, 1997, at 0845 mountain daylight time, a Piper PA-28R-210T, N43761, operated by Altitudes Flight Training, Inc., as a rental, landed with the landing gear retracted at Fort Collins/Loveland Municipal Airport, Fort Collins, Colorado. The private pilot was not injured and the aircraft sustained substantial damage. Visual meteorological conditions prevailed for this personal flight conducted under Title 14 CFR Part 91 and a VFR flight plan, from Englewood, Colorado, to Torrington, Wyoming, was filed. The flight departed Centennial Airport in Englewood at 0815. According to the pilot, he rented the aircraft for the flight and the battery was too weak to conduct a start so the engine start was done using auxiliary power. The pilot said that after departure, when in the vicinity of Jefferson County Airport,(see attached map) he started to get a humming sound in his radios and could not contact Jefferson County Airport Tower. He related that he skirted the control zone and continued to fly in a northerly direction while attempting to find the problem with his radios. He then said he noticed that he had lost all electrical power. When he was flying over the Loveland-Fort Collins Airport, he said he smelled something that he interpreted to be a "hot or burning smell" and decided to land. He stated that he flew a pattern to assure "making" the runway and decided to put the landing gear down at the "last minute." A landing gear retracted landing occurred causing damage to the underside of the fuselage, inboard tips of both flaps, step, and propeller. Investigation revealed that the aircraft alternator was inoperative at the time the aircraft departed on the flight. With the alternator inoperative all electrical power was supplied by the battery and when the battery was depleted, no electric power was available. The landing gear was electric powered as were the landing gear indicators. According to the aircraft flight manual, (applicable pages attached) when a total electrical failure occurs, the landing gear must be lowered using the emergency extension feature and check list. According to the pilot, he was unaware of the emergency extension feature and was not briefed or given a check in the aircraft by the operator. The pilot operator report provided information that the pilot had accumulated 14 hours in this make and model aircraft, but had not flown it in the preceding 30 days and had flown only 2 hours in this make and model in the preceding 90 days.