A B767 WAS DISPATCHED IN NON COMPLIANCE WITH THE ACFT UNABLE TO ACCEPT GND PWR AND AN APU OPERATING WHILE BEING PLACARDED INOP WITH NO LOGBOOK ENTRIES.

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WE HAD AN INOP APU. WE ARRIVED AT XYZ. HAD PROBS WITH GETTING GND PWR. NUMEROUS GPU'S WERE TRIED WITH LITTLE LUCK. ONE DID TAKE AND LASTED UNTIL WE WENT TO START. WHEN WE WENT TO START THE ELECTRIC DIED. THEY COULD NOT GET ANOTHER GPU TO WORK ON OUR ACFT. I WAS TALKING TO MAINT ABOUT BATTERY LIFE AND A BATTERY START; WHEN MAINT WALKED BY AND STATED THE ACFT APU WAS UP AND RUNNING. I RETURNED TO THE ACFT AND WE RAN THE CHKLIST AND STARTED AT THE GATE IN CASE OF ANOTHER PROB. AFTER START THE FO NOTED THE INOP STICKER WAS STILL ON THE APU. THE LOGBOOK SHOWED NO CORRECTIVE ACTION SO WE USED AN INOP SYS TO START. I HAVE MANY MANY QUESTIONS ABOUT EMER BATTERY LIFE AND HOW LONG IT WILL TAKE TO RECHARGE THEM. WHY THE APU WAS PLACARDED AT ZZZ; BUT XYZ WAS ABLE TO START IT AND GET IT WORKING; BUT DID NOT FIX THE LOGBOOK. WHY GATE X AT XYZ HAS BAD ELECTRIC. WHY AFTER CALLING OPS 20 MINS PRIOR TO ARR AND AGAIN ON THE GND TELLING THEM WE HAD NO APU. IT'S A SURPRISE TO THE GND CREW WHEN WE WERE SITTING THERE RUNNING AN ENG WAITING FOR PWR.