A B767-200 IN CRUISE AT FL350 DECLARED AN EMER AND DIVERTS DUE TO LOSS OF CABIN PRESSURE CAUSE UNKNOWN.

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WE WERE DISPATCHED ATL TO DEN AT FL390. ON TAXI OUT; DISCOVERED A PROB WITH THE L AIR CONDITIONING PACK WHERE WE COULDN'T VERIFY IT WAS SHUT DOWN WHEN THE SWITCH WAS PLACED TO 'OFF.' THE LIGHT BULBS CHKED GOOD; BUT THE OVERHEAD PANEL 'PACK OFF' LIGHT AND THE EICAS 'L PACK OFF' MESSAGE WEREN'T WORKING WITH THE PACK IN 'OFF.' THE MECHANICAL DISPATCH MANUAL REQUIRED 1 OF THE 2 INDICATORS TO WORK; SO WE RETURNED TO THE GATE FOR MAINT. MAINT VERIFIED THAT THE L PACK ON/OFF SWITCH APPEARED TO WORK; BUT THEY COULDN'T FIX THE INDICATORS TO READ CORRECTLY. THEREFORE; THEY VISUALLY/MANUALLY VERIFIED THAT THE L PACK WAS SHUT DOWN AND DISPATCHED US TO DENVER WITH ONLY THE R PACK OPERATING. WE WERE DISPATCHED AT FL350 (MAX SINGLE PACK ALT). CRUISING AT FL350; APPROX 10 MINS W OF MEMPHIS; WE RECEIVED A CABIN ALT WARNING (LIGHT; MESSAGE; AND HORN). WE IMMEDIATELY DONNED OUR OXYGEN MASKS AND CHKED THE CABIN WHICH WAS AT APPROX 10500 FT AND CLBING. WE DSNDED SAFELY TO 10000 FT WITHOUT INCIDENT. SHORTLY AFTER WE STARTED THE EMER DSCNT; I TURNED ON THE INOP L AIR CONDITIONING PACK. THE COMBINATION OF THE DSCNT AND THE EXTRA AIRFLOW FROM THE ADDITIONAL PACK PREVENTED THE CABIN FROM EXCEEDING ITS 14000 FT LIMIT. THEREFORE; THE PAX OXYGEN MASKS DID NOT DEPLOY. AT 10000 FT; WE COORDINATED WITH ATC AND DISPATCH AND DIVERTED TO MEMPHIS FOR MAINT INSPECTIONS. WE'RE NOT SURE WHY THE SINGLE R PACK WAS UNABLE TO MAINTAIN THE CABIN. THERE WAS NO INDICATION OF A PACK OR PRESSURIZATION MALFUNCTION (NO AMBER LIGHTS OR EICAS MESSAGES); BOTH AUTO CONTROLLERS APPEARED OPERATIONAL (AND WERE CONFIRMED OPERATIONAL BY MAINT IN MEMPHIS);AND THE OUTFLOW VALVE APPEARED CLOSED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE AIRPLANE WAS CHKED IN MEM BY CONTRACT TECHNICIANS WHO TESTED THE BLEED SYS; AIR CONDITIONING SYS AND PRESSURIZATION CTL AND FOUND ALL SYS TESTED OK. THE RPTR SAID THE AIRPLANE WAS THEN MAINT FERRIED AT 10000 FT TO THE OVERHAUL FACILITY AT ZZZ. THE RPTR STATED HE IS NOT AWARE OF WHAT CORRECTIVE MAINT ACTION WAS TAKEN TO FIX THE PRESSURIZATION RPT.