A STUDENT & INSTRUCTOR (CFI) WERE ON A DUAL X-COUNTRY FLT FM ELROY TO NEILLSVILLE & RTRN. THE FLT TO NEILLSVILLE WAS UNEVENTFULL. AFTER THE ACFT WAS ON THE GND APRX 20 MIN, HOT STARTING PROCEDURES WERE USED TO START THE ENG FOR THE RTRN FLT. ENG RUNUP & TAKEOFF WERE NORMAL UNTIL THE ACFT WAS APRX 150 FT AGL, THEN THE ENG LOST PWR. THE CFI TOOK CTL OF THE ACFT & ATMTD A RESTART WHILE PUMPING THE THROTTLE. HE TURNED RGT ABOUT 30 DEG FOR AN EMERG LNDG. DRG THE LNDG, THE ACFT HIT THE TOPS OF SMALL TREES, ENCOUNTERED SOFT DIRT & NOSED OVER. SUBSEQUENTLY, IT BEGAN BURNING & WAS DESTROYED BY FIRE.DRG THE INVESTIGATION, NO PREIMPACT PART FAILURE OR MALFUNCTION WAS FND THAT WOULD HAVE CAUSED THE LOSS OF POWER. THE PLT BELIEVED THE LOSS OF POWER WAS DUE TO A VAPOR LOCK, BUT THIS WAS NOT VERIFIED. THE PLT RPRTD THE ACFT HAD BEEN SVCD WITH A 50/50 MIXTURE OF 100 OCTANE LOW LEAD FUEL & NO-LEAD AUTO FUEL. LYCOMING SVC INSTRN #1070K DID NOT PERMIT THE USE OF AUTO FUEL DUE TO ITS CORROSIVE EFFECT & BECAUSE OF VAPOR LOCK THAT COULD RESULT FM ITS HI VAPOR PRESSURE.