THE COPLT (DUAL STUDENT) WAS TO GET A PROF CHECK ON THE 1ST LEG OF THE FLT WITH A SIMULATED SINGLE ENG PWR LOSS ON TKOF.ACCORDING TO WITNESSES, THE TKOF WAS NORMAL UNTIL LIFT-OFF APRX 3200' DOWN THE RWY; BUT AFTER LIFT-OFF, THE ACFT CLBD ONLY ABOUT 50' & DIDN'T SEEM TO ACCELERATE. THEY RPRTD THE NOSE PITCHED UP & THE ACFT WENT IN A STEEP BANK ATTITUDE NR THE DEP END OF THE RWY. SUBSEQUENTLY, IT DSCNDD & CRASHED IN WOODED TERRAIN IN A RGT WING DOWN, NOSE HI ATTITUDE. A BY- STANDER TRIED TO GET IN THE ACFT TO RESCUE THE PLTS, BUT THE DOOR WAS JAMMED & HE WAS UNABLE TO BREAK THE CABIN WINDOWS.A FIRE ERUPTED & ENGULFED THE ACFT. DUE TO ROUGH TERRAIN, THERE WAS A DELAY IN GETTING FIRE FIGHTING EQUIPMENT TO THE ACDNT SITE. NO PREIMPACT MECHANICAL FAILURES WERE FND. THE GEAR, FLAPS & SPOILERS WERE FND IN THE RETRACTED PSN. FOR TKOF, THE FLAPS SHOULD HAVE BEEN EXTD TO THE 8 OR 20 DEG POSITION. THE STALL SPEEDS FOR 20 DEG, 8 DEG & NO FLAPS WERE 104.5, 109.0 & 119.5 KTS, RESPECTIVELY. THE CAPT WAS AN FAA DESIGNATED FLT EXAMINER & A CERTIFIED FLT INSTRUCTOR (CFI).