On June 23, 2003, about 1950 central daylight time, a Beech BE-35-33, N929TP, registered to and operated by a private individual as a Title 14 CFR Part 91 instructional flight, crashed shortly after takeoff from Raymond, Mississippi. Visual meteorological conditions prevailed, and no flight plan was filed. The private-rated pilot received minor injuries, and the commercial-rated flight instructor received serious injuries. The airplane incurred substantial damage. The flight was originating at the time of the accident. The pilot stated that prior to departing on his flight, he visually ensured that the both auxiliary fuel tanks were full of fuel, and then he and his flight instructor topped off the main fuel tanks. After waiting several minutes, the pilot said that he checked the fuel sumps, and took off about 1815. He said that the fuel selector valve was set to the left main fuel tank position, and they flew to the practice area and performed several maneuvers. They then proceeded to Hawkins Field and performed two ILS approaches to runway 16. By that time he said that they had burned about 1/2 the fuel in the left main tank and they changed the fuel selector to the "auxiliary tanks position." They then flew across the reservoir to view some land in Rankin County, and after looking at the land, flew back to the Raymond Airport, and entered a left downwind for landing on runway 12. He also specifically said that he on the downwind he placed the fuel selector to the right main fuel tank position. He said they flew the approach and performed a touch-and-go landing on runway 12, and then flew a left pattern and practiced slips to a landing. He said they practiced slips "both ways" to a landing on runway 12, and performed another touch-and-go landing. About 1945, and the pilot said he was taking off after a touch-and-go landing, and when he reached an altitude of 200 feet during the climb, the airplane's engine ceased operating. He said that the flight instructor took over control of the airplane, and they both worked together to perform emergency procedures in an attempt to restart the engine. He stated that as part of the emergency procedures, they ensured that the fuel selector was set to the right main fuel tank, and that the fuel gauge showed that there was fuel onboard. As they were descending and approaching the trees, the pilot said that the flight instructor told him to activate the auxiliary pump, and when he did so the airplane engine began operating again. He said the engine operated sufficiently to clear the trees, and then ceased operating again. While over the trees, the pilot said the airplane stalled, and it descended, impacting the ground. The flight instructor did not provide a statement to the NTSB. Postcrash examination of the aircraft was performed by an FAA licensed mechanic with an inspection authorization rating. The mechanic stated that the fuel system was intact and that there was no evidence of fuel leakage. He further stated that he found about 1/3 to 1/2 of a tank of fuel in the auxiliary tanks, about 2/3 a tank of fuel in the left main tank, and the right main fuel tank was full. During recovery of the airplane, the mechanic said that the airplane was placed on the flat-bed truck, with the landing gear retracted. He said that while on the flat-bed, the airplane was in a slightly nose high attitude, and he noted that the auxiliary fuel tank's fuel supply opening which supplies fuel from the auxiliary fuel tank to the engine was uncovered, with the fuel in the auxiliary tanks being below the opening. The mechanic also stated that under the supervision of an FAA inspector, he verified the integrity of all pertinent airplane systems. He stated that he verified delivery of fuel to the engine. He said he installed the battery, grounded the airplane, and operated the fuel pump and checked fuel flow from all tank positions. He also said he checked fuel tank vents for obstructions, checked fuel screens, and removed and examined the fuel pump. He then reinstalled the fuel pump, and rigged the engine to a test stand, testing it throughout the full operating range, and it operated normally.