A B777-200 L ENG CONTACTED THE JETBRIDGE DURING POSTFLT TAXI INTO PARKING FOLLOWING A TAXI DIRECTOR'S GUIDANCE.

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AFTER LNDG; WE WERE INFORMED BY OUR OPS PERSONNEL THAT WE WERE ASSIGNED A GATE FOR PARKING AND THAT THE GATE WAS OCCUPIED BY A B757 THAT HAD A MECHANICAL PROB. WE WERE TOLD THAT THE GND CREW WAS GOING TO PUSH THE ACFT OFF THE GATE IN 5 MINS. WE WERE INSTRUCTED BY HNL GND CTL TO HOLD OUR POS ON TXWY Z JUST W OF TXWY K (FACING W) AND WAIT FOR THE GATE TO CLR. AFTER APPROX 5 MINS; WE OBSERVED THE B757 BEING PUSHED OFF THE GATE AND BEING TOWED WBOUND ON TXWY Z WHILE A UNIFORMED MALE RAMP EMPLOYEE WAS STANDING ON THE GATE CTRLINE WITH ORANGE WANDS IN HIS HANDS READY TO GUIDE US INTO THE GATE AREA. AS THE B757 CLRED THE GATE ENVELOPE; WE WERE INSTRUCTED BY HNL GND CTL TO TAXI TO THE GATE. WE BEGAN TO APCH THE GATE AREA AND WE WERE CONTINUALLY UNDER POSITIVE GUIDANCE OF THE GUIDEMAN AND FOLLOWED HIS SIGNALS. AS WE APCHED THE NORMAL STOP POINT; WE HEARD A 'THUD' AND FELT AN ACCOMPANYING ACFT VIBRATION. THE GUIDEMAN THEN SIGNALED A STOP AND DISAPPEARED FROM VIEW; UNDER THE ACFT NEVER TO BE SEEN AGAIN. SINCE WE DID NOT KNOW WHAT HAD OCCURRED; I OPENED THE COCKPIT WINDOW AND ATTEMPTED UNSUCCESSFULLY TO GAIN THE ATTN OF THE GND CREW. WE CONTACTED STATION OPS VIA RADIO AND THEY INFORMED US THAT WE MAY HAVE STRUCK THE JETBRIDGE. WE IMMEDIATELY CONTACTED HNL GND CTL AND ADVISED THEM OF THE POSSIBLE COLLISION AND REQUESTED THEY DISPATCH THE FIRE CREW TO INSPECT THE ACFT FOR DAMAGE. WE SECURED THE ENGS AND NOTIFIED THE FLT ATTENDANTS OF THE PROB VIA A FLT INTERPHONE 'ALL CALL.' WE REQUESTED THEIR ASSESSMENT OF THE SIT AND REQUESTED THE STATUS OF THE PAX AND WE WERE INFORMED THAT NO ONE ON BOARD WAS INJURED. WE ADVISED THEM TO ENSURE THAT ALL DOORS REMAINED ARMED AND TO EXPECT TO SEE THE FIRE DEPT SHORTLY. WE MADE A PA ANNOUNCEMENT TO ADVISE THE PAX OF THE SIT AND THEY ALL APPEARED TO BE UNDERSTANDING AND NO ONE HAD ANY COMPLAINTS OF INJURY DURING THE DEPLANING PROCESS. THE LACK OF GND CREW COMS WITH US IMMEDIATELY AFTER THE COLLISION WAS MOST DISTURBING. IF THE COLLISION HAD CAUSED MORE DAMAGE TO THE ENG OR SYS; WE COULD HAVE HAD A SERIOUS FIRE DUE TO THE FACT THAT PRECIOUS SECONDS WERE ALLOWED TO PASS BEFORE WE HAD ANY IDEA THAT AN OPERATING ENG HAD IMPACTED THE JETBRIDGE. THE GND CREW SHOULD HAVE GAINED OUR ATTN VIA ANY MEANS POSSIBLE AND INDICATED TO US TO SHUT DOWN THE ENG. A POSTFLT INSPECTION REVEALED THE L ENG COWL HAD STRUCK THE SOUTHERNMOST JETBRIDGE.