THE ACFT WAS ON AN FAA CERTIFICATION FLT (EXPERIMENTAL). DURING THE RECOVERY PHASE, A NON-TYPE RATED FAA PLT WAS IN THE L SEAT & THE PIC WAS IN THE R SEAT. WHILE DESCENDING, A DUCT FAIL LGT & A LEADING EDGE OVERHEAT LGT CAME ON. THE PIC TOOK CORRECTIVE ACTION. THE FAA PLT MADE AN ILS APCH TO RWY 22 WHICH WAS WET. THE APCH WAS MADE WITH THE L ENG AT HI IDLE. THE THRUST REVERSERS WERE NOT ARMED FOR THE LANDING. A TOUCHDOWN WAS MADE ABOUT 2000' DOWN THE RWY & SPOILERS WEREDEPLOYED. WHEN THE FAA PLT REALIZED HE DID NOT HAVE REVERSE THRUST, HE TRIED SLOWING THE ACFT WITH BRAKES; HOWEVER, THE L BRAKE WAS INOP. THE PIC TOOK CONTROL & CYCLED THE ANTI-SKID, BUT STILL HAD NO L BRAKING ACTION. SUBSEQUENTLY, THE ACFTRAN OFF THE END OF THE RWY & THE NOSE GEAR COLLAPSED IN MUDDY TERRAIN. AN INVESTIGATION REVEALED THAT DURING MAINTEN- ANCE, THE SPEED SENSOR HARNESSES FOR THE L MAIN GEAR WERE REVERSED WHICH ELIMINATED ANY BRAKING TO THE L BRAKE WHILE THE ANTI-SKID WAS ON.