WHILE ATTEMPTING TO LAND DOWN WIND ON A PRIVATE SOD STRIP, DURING AN AERIAL APPLICATION OPERATION, THE COMMERCIAL PILOT LOST DIRECTION CONTROL, GROUND-LOOPED, THEN VEERED OFF THE RUNWAY AND NOSED OVER. THE PILOT STATED THAT HE ATTEMPTED TO REGAIN CONTROL WITH BRAKING, BUT FELT THAT HE HAD NO BRAKES. INVESTIGATION FAILED TO REVEAL ANY BRAKE MALFUNCTION.