AN AIRBUS 320 INCURRED LEADING EDGE SLAT DAMAGE WHEN TOWED ONTO A GATE STRIKING AN IMPROPERLY PARKED JETWAY.

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I PUSHED ACFT XYZ ACR ABC WHICH ACR IS CONTRACTED TO PUSH BACK FROM GATE BEFORE DISCONNECTING TOW BAR FROM ACFT. I GAVE THE CAPT TO START ENGS SO HE ATTEMPTED TO START R-HAND ENG. HE RPTS NOT ENOUGH AIR PRESSURE TO START. I TOLD HIM TO SHUT DOWN HIS AIR PACKS; STILL NOT ENOUGH AIR. HE TELLS ME TO PULL BACK TO GATE AND GET A STARTER TRUCK TO START ENG. I PULLED THE ACFT TO GATE. I OVERSHOT THE MARKS. I WAS GOING IN REVERSE. WHEN I LOOKED FORWARD THE ACFT WAS 10 INCHES FROM THE LOADING BRIDGE. I APPLIED MY BRAKES BUT MOMENTUM TOOK ME INTO THE BRIDGE. ACFT STRUCK THE BRIDGE MADE A 2 INCH BY 6 INCH HOLE IN THE LEADING EDGE BTWN #2 LEADING EDGE SLAT AND INBOARD SLAT ON THE STATIONARY PIECE ABOVE #1 ENG PYLON. WITH PRODUCTION PERMIT FROM ABC MAINT WE TAPED OVER THE HOLE AND DEFERRED THE MAINT TO VANCOUVER; BC. IT TURNED OUT THE CREW WAS NOT FAMILIAR AT TO START ENG WITH A WING ANTI VALVE WIRED IN THE OPEN POS THEREFORE MOST OF THE AIR PRESSURE WAS BEING DUMPED INTO THE R-HAND WING ANTI-ICE. IF THE CREW KNEW ABOUT ISOLATION OF THE R-HAND WING ANTI-ICE; WE WOULD HAVE HAD ENOUGH AIR PRESSURE TO START ENGS.