According to one of the pilots of the Cessna 177RG, during the preflight inspection, he observed approximately 35 gallons of fuel onboard. The other pilot sumped the fuel tanks and no water was present. After engine start, runup was "normal," and the pilots completed the pre-takeoff checklists with no anomalies noted. After takeoff, the pilot at the controls retracted the landing gear and "immediately" observed a "very noticeable" drop in rpm and airspeed. With insufficient runway remaining, he made a slight turn to avoid obstacles at the end of the runway, lowered the landing gear, extended the flaps, and reduced power. The airplane impacted terrain, bounced back into the air, and impacted trees. The airplane came to rest nose-down at the base of a tree. The pilots exited the airplane, and because of a strong odor of fuel, turned the fuel selector to the "off" position, and turned off the master switch. Neither the pilots nor the on-scene Federal Aviation Administration inspector reported any mechanical anomalies on scene. The inspector also confirmed cylinder compression and spark from the dual magnetos. The airplane was subsequently moved to a salvage yard, where an engine run was performed under Safety Board oversight. The engine started after 5 to 6 turns, and ran for about 5 minutes. During magneto checks, the left magneto of the dual magneto appeared to be operating abnormally, resulting in increased engine shaking as the rpm was increased. The engine ran normally on the right magneto.