On October 16, 2016, at 1205 central daylight time, a Bellanca 17-31A, N93668, experienced a loss of engine power during climb from a touch-and-go landing on runway 20 at Mc Alester Regional Airport (MLC), Mc Alester, Oklahoma. The airplane sustained substantial damage. The flight instructor and a private pilot/airplane owner received serious injuries. The airplane was newly registered to and operated by the pilot under Title 14 Code of Federal Regulations Part 91 as an airplane checkout instructional flight. Day visual meteorological conditions prevailed at the time of the accident. The flight originated from Sundance Airport (HSD), Oklahoma City, Oklahoma, about 0930. A National Transportation Safety Board Pilot/Operator Accident/Incident Report (form 6120.1) was not received from the pilot. According to the Federal Aviation Administration Coordinator for the accident, the flight was for the purposes of an aircraft checkout and flight review for the pilot. An aircraft bill of sale showed the pilot as the purchaser of the airplane and was dated October 13, 2016. The flight instructor stated, in his form 6120.1, that the airplane was preflighted and topped off with fuel at HSD. He stated that his flight planning calculations indicated there would be 30 gallons of fuel remaining upon arrival at MLC. He stated that the flight departed at 0930 and was flown to Ponca City Regional Airport (PNC), Ponca City, Oklahoma, where an instrument approach and a touch-and-go landing were performed. He then flew to Tulsa International Airport (TUL), Tulsa, Oklahoma, where a touch-and-go landing was performed, followed by a flight to MLC. The flight instructor stated that during a visual approach to MLC, the left fuel tank was selected since it was the fullest tank. The flight instructor stated that at MLC, the fuel gauges indicated the left fuel tank was less than ½ full, and the right fuel tank was above ¼ full. The auxiliary fuel tank was full. After a touch-and-go landing on runway 20, the airplane experienced a loss of power while climbing through 100 feet above ground level. The flight instructor told the pilot to fly a best glide speed. The flight instructor verified that the fuel selector was positioned to the left fuel tank, the mixture was full rich, and the propeller and throttle were in their full forward positions. The flight instructor stated that about two seconds elapsed from the time of the engine power loss to his flaring the airplane for landing. Post-accident examination revealed the airplane touched down on a field about 200 feet south of the departure end runway 20. The airplane impacted terrain upright and slid 30-40 feet sustaining substantial damage to both wing spars; no post-impact fire ensued. Damage to the propeller blades were consistent with torsional rotation. The left and right tanks contained no useable fuel. The auxiliary fuel tank was approximately full. The main fuel supply line from the fire wall to the gascolator, to the engine driven pump, to the fuel servo and to the flow divider were disconnected to check for the presence of fuel, and no or only several drops of liquid consistent in odor with aviation fuel was present. These lines were intact and not broken open. The bottom fuselage area near the fuel selector sustained impact damage, and the fuel lines were separated at the fuel selector valve fittings. The gascolator screen did not contain debris, and the gascolator bowl contained a few drops of liquid consistent in odor with aviation fuel. Post-accident examination of the fuel selector was unable to determine selector position due to shifting during impact. The pilot stated that he could not detect the fuel detent and moved the selector to the left fuel tank position using the position indicator light as a reference. The airplane total time at the last annual inspection was 2,724.15 hours. The engine was a Lycoming IO-540-K1E5 with serial number L-11719-48. The airplane total time since new at the annual inspection was 2,489.15 hours. The tachometer reading at the accident site was 2,480.20 hours. The engine was rotated through and air was drawn into and expelled from the bottom spark plug holes after these spark plugs were removed. The compression exhibited during engine rotation by hand through the bottom spark plug holes was low. Engine and valve train continuity to the accessory section was confirmed. Both magnetos were rotated and electrical continuity through the ignition harness was confirmed. The left turbocharger was Garrett Allied Signal, part number 600572-00, serial number 1245 and the right turbocharger was Rajay Industries, part number 315 F 10-2, serial number 2544. Both turbocharger impellers were able to be rotated by hand. There was no record that the turbochargers had been overhauled since the original engine installation at the time that the airplane was manufactured. The turbocharger exhaust bypass valves contained dirt and debris. The exhaust pipes were corroded to a thickness consistent with an unairworthy condition. Duct and packing tape was used to secure a piece of engine baffle to the front of the engine. The engine had safety wire installed in place of required hardware that included cotter pins, nuts, bolts and washers. A post-accident calibration check of the fuel tank transmitters was not performed. The flight instructor stated the he "trusted" the airplane owner's maintenance of the airplane. The flight instructor stated that he did not use the electric auxiliary fuel pump during selection of fuel tanks from the right main fuel tank to the left main fuel tank. He did not attempt use the electric auxiliary fuel pump following the engine power loss because of the elapsed time from the engine power loss to landing the airplane. He said that the use of the electric auxiliary fuel pump would not have remediated fuel because there was not enough time available for it to take effect. He said that he now teaches to change fuel tank selection outside of the airport traffic pattern because the engine is operating at a greater fuel flow demand than in the traffic pattern. The airplane operations manual states that the electric auxiliary switch is provided for only starting and in the event the engine driven fuel pump fails. The operations manual checklist for landing states that the fuel selector is to be selected to the fullest tank.