What was found
LANDED IN KJAC AT 0224 Z AND TAXIED TO JACKSON HOLE AVIATION RAMP. SET PARKING BRAKE AND SUTDOWN ENGINES 1 AND 3. BRIEFED COPILOT TO LEAVE THE PARKING BRAKE ON AS IT WAS NONSTANDARD PROCEDURE AFTER BEING CHICKED. THE RAMP AGENT POINTED TO THE LEFT MAIN GEAR AND I OBSERVED HYDRAULIC FLUID. I LOOKED INTO COCKPIT AND OBSERVED SYSTEM 1 HYDRAULIC QUANTITY TO BE AROUND 1/4 OF NORMAL QUANTITY AND PRESSURE TO BE 0. SYSTEM 2 HYDRAULIC QUANTITY WAS NORMAL AND PRESSURE 3000. I GOT INTO THE COCKPIT TO ASSESS WHAT WAS GOING ON WITH THE HYDRAULICS. THE RAMP AGENT MUST HAVE PULLED THE CHALKS BECAUSE AS SOON AS I GOT TO COCKPIT, I NOTICED THE PLANE WAS ROLLING OR SLIDING FORWARD AT A SLOW WALK SPEED. I PRESSED THE FOOT BRAKE PEDALS, THE PLANE KEPT MOVING. I SELECTED BRAKES 2 POSITION AND USED THE PDALS, THE PLANE KEPT MOVING. I THEN REACHED UP FOR THE HAND PARKING BRAKE, BUT IT WAS ALREADY FULLY ENGAGED. I THEN DEPLOYED THE THRUST REVERSER AND WAS ABLE TO STOP THE PLANES FORWARD MOVEMENT, BUT WE STARTED TO MOVE BACKWARDS SO I STOWED THE THRUST RESERSER TO SHUT DOWN THE ENGINE, BUT WE STARTED MOVING FORWARD AGAIN. AS WE ROLLED/SLID FORWARD, AT SLOW WALK SPEED, I TRIED TO STEER THE NOSE AND BRAKE, BUT WE CONTINUED STRAIGHT. I CONTINUED TO SHUT DOWN ENGINE 2 AS THE REVERSER WAS NOT DEPLOYED ENOUGH TO GIVE US REVERSE THRUST WE CONTINUED TO ROLL / SLIDE AT SLOW WALK SPEED, WITH THE CONTOUR OF THE RAMP AND THE RIGHT WING OUTBOARD SLAT MADE CONTACT WITH THE NOSE GEAR DOOR OF A CITATION N680DJ, AND THE LEFT WING OUBOARD SLAT MADE CONTACT WITH THE NOSE RADOME OF PHENOM N352FX. BOTH OUTBOARD SLATS REPLACED WITH SERVICEABLE. LEFT NOSE GEAR DOOR REPLACED WITH SERVICEABLE. LEFT INBOARD BRAKE REPLACED WITH LOANER BRAKE.