AN MD88 IN CRUISE AT FL330 DIVERTED DUE TO MAIN SHIP'S BATTERY DISCOVERED AT ZERO BOLTS CAUSED BY A FAILED CLOSED APU START RELAY.

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I WAS CAPT ON ACR FLT XXX ON DEC/XA/00 SCHEDULED TO GO FROM SNA TO SLC. DURING CLB TO FL330 PASSING FL290; STATUS LIGHT CAME ON OVERHEAD ANNUNCIATOR PANEL. MESSAGE WAS ACFT STATUS FAULT. WHILE REFING OUR OPS MANUAL; WE NOTICED THE CLOCK FAIL MESSAGE ON MCDU SCRATCH PAD. THIS WAS FOLLOWED SHORTLY BY THE INERTIAL REF SYS-1 BATTERY FAIL AND THE BATTERY FAIL LIGHT ON THE IRU PANEL. WHEN WE REFED THE PROC; A NOTE SAID TO CHK THAT THE BATTERY SWITCH WAS ON. THE BATTERY SWITCH WAS ON; BUT WHEN WE CHKED THE VOLTS AND AMPS FROM THE BATTERY THEY WERE BOTH AT ZERO. ABOUT THIS TIME THE BATTERY BUSS OFF MESSAGE ILLUMINATED. WHEN WE TESTED THE ANNUNCIATOR/DIGITAL LIGHTS AND CHKED THE AC AND DC EMER BUSS OFF LIGHTS THEY WERE NOT ILLUMINATED. THIS INDICATES BATTERY PWR IS NOT AVAILABLE AND THE PROC ENDED WITH THE LAND AT NEAREST SUITABLE ARPT INSTRUCTION. WE WERE JUST PAST LAS AND I WAS TALKING TO MAINT ON ZZZ RADIO FREQ. I INFORMED THEM OF THE PROC AND MY INTENTION TO DIVERT TO LAS AND THEY CONCURRED. ATC; FLT ATTENDANTS AND PAX WERE INFORMED. WE LANDED SAFELY IN LAS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE FIRST WARNING OF BATTERY PROBS WAS AN OVERHEAD ANNUNCIATOR PANEL STATUS MESSAGE. THE RPTR SAID THE ACFT STATUS MESSAGE LED TO THE CLOCK FAIL FOLLOWED BY THE INERTIAL REF SYS BATTERY FAIL LIGHT. THE RPTR SAID WHEN CHKING THE BATTERY VOLTS AND AMPS; IT WAS THEN DISCOVERED THE BATTERY WAS DEAD.