FLC OF A B757 LOST HF COMS ON AN OVERWATER ENRTE TO FOREIGN DESTS DUE HF RADIO MALFUNCTION. CAPT DECIDED TO CONTINUE TOWARD DEST SINCE THERE WAS ONLY A SHORT DSCNT TO VHF COVERAGE EVEN THOUGH COMPANY FLT MANUAL INSTRUCTED TO CONTACT DISPATCHER FOR REROUTING FLT.

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WE ARRIVED AT FLT XXX 30-40 MINS AFTER SCHEDULED DEP. FOLLOWING FLT ATTENDANT BRIEFING AND WALKAROUND INSPECTION; FO AND I SET ABOUT COCKPIT PREPARATION. NUMEROUS INTERRUPTIONS OCCURRED BUT WE FINISHED. AS WE COMPLETED THE CHKLIST AND WERE ENTERING 'FINAL AWABS' EXTERNAL PWR WAS PULLED BEFORE APU UP TO SPD AND ALL DATA WAS LOST. PRESENT POS WAS LOST SO THE FO INITIATED A NEW ALIGNMENT. WHILE WE WAITED; WE CLRED UP SEVERAL CABIN; CREW AND BRIEFING ITEMS. ONE OF THESE WAS AN HF CHK. WHILE WE COULD WEAKLY HEAR OTHER CALLS THERE WAS NO RESPONSE TO OUR REQUESTS. BOTH FO AND I COULD HEAR ME XMITTING. I NEXT TRIED A VHF (ATC) SELCAL CHK JUST TO BE SURE WE COULD XMIT AND RECEIVE; AND RECEIVED SELCAL. 1 HR 19 MINS LATE WE DEPARTED ATL FOR MPTO (PANAMA). PASSING FL180 WE ACCOMPLISHED THE VHF CHK AND I DECIDED TO TRY AN HF SELCAL CHK. FO CALLED FOR A NAV ACCURACY AND MAGNETIC COMPASS CHK. I PERFORMED AS REQUESTED AND FORGOT THE HF CHK. LATER IN OUR FLT AFTER PASSING MONTEGO BAY; I REMEMBERED THE FAILURE TO GET THE SELCAL CHK (THE VOLUME ON THE HF WAS ON BUT VERY LOW). I TURNED UP THE VOLUME AND MADE A NUMBER OF XMISSIONS WITH NO RESPONSES. WE COULD HEAR OTHER PLANES WEAKLY ON NEW YORK AND HOUSTON FREQS. NEXT I TRIED CARIBBEAN HF FREQS AND COULD HEAR LOUD SPANISH XMISSIONS BUT DID NOT GET ANY ANSWERS. WE HAD FULL COM WITH KINGSTON CTR AS WE CONTINUED OUTBOUND TOWARD PANAMA. WHILE FO FLEW; I REFED MY FLT OPS MANUAL AND COMMERCIAL CHARTS TO SEE WHAT NEEDED TO BE DONE. LATER IN MY READING; I FOUND A REF THAT SAID IF HF INOP TO COORDINATE WITH DISPATCH TO BE ROUTED SO AS TO STAY IN VHF RANGE. (IN OTHER WORDS; WE PROBABLY SHOULDN'T BE WHERE WE WERE.) AT THAT TIME I DECIDED THE DISTANCE THAT WE WOULD BE OUT OF VHF CONTACT WOULD BE SMALL AND SINCE WE WERE MONITORING HF GUARD WE WOULD HEAR ANY XMISSIONS AND COULD XMIT ON ACARS. I FELT IT WOULD BE MORE HAZARDOUS TO TURN AROUND AT THAT POINT. SIMPLY PUT; I SHOULD NOT HAVE FORGOTTEN THE HF CHK UNTIL SO LATE INTO THE FLT AND SHOULD HAVE BEEN MORE CONCERNED WITH THE INCOMPLETE CHK ON THE GND. COMPANY PROC DOES ALLOW DISPATCH IF BOTH PLTS CONFIRM THAT WE SOUND LIKE WE ARE XMITTING.