During the initial climb, the airplane attained an altitude of approximately 200 feet AGL when the engine lost partial power and the CFI noted a low fuel flow. The CFI ordered the second pilot to reduce power, which the pilot did. The CFI then decided that there wasn't sufficient room left to land on the remaining runway and ordered the second pilot to add full throttle and activate the electric fuel pump to try and restore power to go-around. The CFI took over the controls and made a right turn away from the runway. Power was not restored and the CFI made a forced landing off the runway. The airplane touched down in a grassy area between runways, travelled across another runway and collided with a ditch on the opposite side. The airplane came to rest inverted. During the post-crash inspection, the engine was prepared for an engine run. The engine started immediately and was run for several minutes, with no indication of a mechanical failure or malfunction.