During the pre-take off checks the student found the carburettor heat control could be pulled out further than usual and that there was no rpm drop associated with the application of hot air. On take-off the aircraft was slow to accelerate. It became airborne and was observed to enter a gentle right turn. A wing dropped and the aircraft impacted the ground. Investigation revealed that due to excessive wear, the carburettor heat control cable had failed at the attach point with the actuating bellcrank. The air hose between the muffler and the carburettor hot air box had collapsed internally. The combination of the carburettor heat control failure in the "hot" position and the obstruction of the alternate air source led to the loss of engine power during take-off. Shortly afterwards the aircraft stalled over flat open country.