B767 FLT CREW EXPERIENCE A L GENERATOR TRIP OFF LINE. THEY ARE UNABLE TO GET APU STARTED SO THEY RETURN TO LAX AFTER RESETTING THE GENERATOR. MAINT OPS CHKED THE APU OK. AFTER DEP; THE FLT CREW COULDN'T START THE APU UNLESS HOLDING THE START BUTTON.

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AS THE GEAR WAS RETRACTED; THE L GENERATOR TRIPPED OFF LINE. I ASKED FOR THE APU TO BE STARTED. IT DID NOT START. WE GOT THE FLT MANUAL OUT AND PROCEEDED WITH THE APPROPRIATE CHK FOR THE L GENERATOR. WE ACCOMPLISHED THE PROC AND GOT THE L GENERATOR BACK. WE THEN ATTEMPTED ANOTHER APU START; BUT THERE WAS NO ROTATION. ALL OUR INDICATIONS SHOWED NORMAL START SEQUENCING; BUT NO ROTATION. WE DECIDED TO RETURN TO LAX. MAINT SVCED THE L IDG WITH OIL; CHKED AND STARTED THE APU. A NEW MAINT RELEASE WAS GENERATED WITH THE INSTRUCTION TO START THE APU INFLT FOR ETOPS VERIFICATION. WE DEPARTED LAX AGAIN. AFTER CLBING THROUGH FL240; WE ATTEMPTED ANOTHER APU START. AGAIN; ALL INDICATIONS SHOWED NORMAL START SEQUENCING BUT NO ROTATION. WE CONTINUED OUR CLB TO FL340. WE CONTACTED DISPATCH AND DECIDED WE WOULD TURN BACK FOR LAX AGAIN IF WE COULD NOT GET THE APU STARTED. WE TRIED ONE LAST ATTEMPT BUT THIS TIME I HELD THE START SWITCH IN START AND IMMEDIATELY APU N2 INDICATION (ON STATUS PAGE) STARTED ROTATING. NORMAL ACCELERATION AND EGT RISE WAS OBSERVED. WHEN APU REACHED 100% THE RUN LIGHT CAME ON STEADY; I RELEASED THE START SWITCH AND THE APU RAN NORMALLY. WE LEFT IT ON FOR ABOUT 25 MINS. WE NOTIFIED DISPATCH THAT THE APU WAS UP AND RUNNING. WE WERE STILL ABOUT 20 MINS FROM ENTERING ETOPS AIRSPACE. DISPATCH ASKED FOR CONFIRMATION THAT THE APU WAS RUNNING. WE TOLD HIM IT WAS. HE SENT US OUR ETOPS WX. WE CONTINUED TO HNL.