B737 FLT CREW REPORTS CABIN ALTITUDE WARNING HORN AT FL360 AND INITIATES DESCENT TO 10000 FEET. EMERGENCY DECLARED WITH DIVERT TO NEAREST SUITABLE ARPT.

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UPON ARR AT THE GATE; MAINT PERSONNEL WERE CALLED OUT BY THE PREVIOUS FLT CREW TO CHK ON CONDENSATION COMING FROM THE OVERHEAD VENTS IN THE CABIN. IT WAS DETERMINED THAT IT WAS A NORMAL CONDITION DURING HIGH HUMIDITY; AND SUBSEQUENTLY THERE WAS NO WRITE-UP IN THE LOGBOOK. I ACCEPTED THE ACFT. APPROX 1 HR INTO THE FLT AT FL360; AND IN CRUISE FLT; WE HAD THE CABIN ALT WARNING SOUND. WE PUT ON OUR MASKS AND SET UP THE AUDIO SO WE COULD HEAR EACH OTHER. WE ALSO ASKED FOR A LOWER ALT AND STARTED A SMART DSCNT TO FL240. I RAN THE CABIN ALT WARNING CHKLIST DURING THE DSCNT; AND AFTER SELECTING THE PRESSURIZATION MODE SELECTOR TO MANUAL AND CLOSING THE OUTFLOW VALVE; I NOTICED THE CABIN WAS STILL CLBING AT APPROX 500 FPM; EVEN THOUGH THE OUTFLOW VALVE WAS INDICATING CLOSED. WE DECLARED AN EMER IN ORDER TO GET DOWN TO 10000 FT. DURING THE DSCNT; I FIRED OFF A FEW ACARS MESSAGES TO DISPATCH NOTIFYING THEM OF OUR SITUATION; AND THAT WE WERE DSNDING TOWARD ZZZ1. WE RECEIVED 2 MESSAGES FROM DISPATCH ASKING IF WE WERE DIVERTING BACK TO ZZZ. THIS SEEMED ODD SINCE WE WERE NO WHERE NEAR ZZZ. I ATTEMPTED VOICE COM AND AS IT TURNS OUT AT 10000 FT WE WERE TOO LOW TO COMMUNICATE. IT IS IMPORTANT TO NOTE THAT AT SOME POINT DURING OUR DSCNT AT APPROX THE MIDDLE TEENS IN ALT; THAT I WAS SPRAYED WITH ABOUT A HALF OF CUP OF WATER THROUGH OUR EYEBALL COCKPIT VENTS. AFTER CLRING MY VISION; I LOOKED UP AND NOTICED THE CABIN RATE INDICATOR WAS SHOWING THE CABIN DSNDING IN EXCESS OF 3500 FPM FOR A FEW SECONDS FOLLOWED BY AN INCREASE OF CABIN ALT OF 2500 FPM BEFORE FINALLY SETTLING AUTO ON THE CTLR SET IN ZZZ1 ELEVATION; AND THE SYS SEEMED TO BE WORKING AGAIN. THE HIGHEST CABIN ALT NOTICED WAS 11500 FT AND THE MASKS DID NOT DROP. I SENT ANOTHER ACARS TO DISPATCH INDICATING OUR INTENTION TO LAND AT ZZZ1. THEY CONCURRED AND WE LANDED AT ZZZ1 WITHOUT FURTHER INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: SINCE THE SYSTEM SEEMED TO BE FULLY FUNCTIONAL DURING AND AFTER LANDING; MAINTENANCE WAS UNABLE TO FIND ANY FAULTS. THE ACFT WAS FERRIED WITHOUT REPAIRS AND FUNCTIONED NORMALLY. WATER IS STILL THOUGHT TO BE EITHER A CAUSE OR A SYMPTOM OF THE PROBLEM.