DURING ARRIVAL, THE ACFT WAS LANDED ON RWY 6 ON A DARK NIGHT. THE PLT STATED THAT THE AIRSPEED INDICATED 85 KTS AS THE ACFT WAS OVER THE RWY NUMBERS, AND AFTER A NORMAL LANDING, HE APPLIED BOTH BRAKES. HE REPORTED THAT AS SOON AS HE APPLIED BRAKES, THE ACFT BEGAN A RIGHT TURN AS IF THE BRAKES LOCKED. HE RELEASED THE BRAKES & APPLIED LEFT BRAKE & RUDDER, BUT THERE WAS NO RESPONSE. THE ACFT CONTINUED SKIDDING SIDEWAYS, WENT OFF THE RIGHT SIDE OF THE RWY & COLLIDED WITH 2 PARKED ACFT; A PIPER PA-28, N4842L & A GRUMMAN AMERICAN AA-5, N5462L. AN INVESTIGATION REVEALED THAT THE SKID MARKS BEGAN APRX 1900 FT FROM THE APCH END OF THE 2580 FT RWY. MEASUREMENTS OF 3 SKID MARKS ON THE RWY REVEALED THAT THE PLANE SKIDDED 272 FT WHILE ANGLED UP TO 35 TO 40 DEG FROM THE RWY HEADING. AFTER DEPARTING THE RWY, THE PLANE SKIDDED ANOTHER 262 FT BEFORE STRIKING THE OTHER 2 ACFT. THE PASSENGER (A STUDENT PLT) IN THE COPILOT'S SEAT ADMITTED HE APPLIED THE BRAKES ON HIS SIDE WHEN HE SAW THAT THE ACFT WAS DEPARTING THE RWY.