THE STUDENT MADE 3 FULL STOP LANDINGS ALONE BEFORE THE INSTRUCTOR BOARDED THE ACFT. ANOTHER FULL STOP LANDING WAS MADE AND DURING THE LANDING ROLL THE INSTR NOTICED THAT THE LAST HALF OF THE GRASS RWY WAS WETTER THAN THE FIRST HALF. THE INSTR ELECTED TO TAKEOFF & LAND IN THE OPPOSITE DIRECTION; TO THE EAST. ON THE FIRST LANDING TO THE EAST, FULL FLAPS WERE USED AND THE APCH SPEED WAS 80 KTS. THE ACFT TOUCHED DOWN HALF WAY DOWN THE RWY. ABOUT 1700 FT OF RWY REMAINED WHEN THE BRAKES WERE APPLIED. ACCORDING TO THE INSTR, THE ACFT SLOWED DOWN IN A NORMAL MANNER UNTIL SOON AFTERWARDS THE STU STATED HE HAD LOST BRAKES. THE INSTR ATTEMPTED TO GROUND LOOP THE ACFT. HOWEVER, WHEN HE TRIED, THE ACFT SKIDDED INSTEAD OF TURNING AND WENT OFF THE RWY INTO A RAVINE AND NOSED OVER. EXAMINATION OF THE ACFT REVEALED THAT THE BRAKES WERE INOPERATIVE.