FLC OF AN LGT ACR ACFT DECLARED AN EMER AND MADE AN EMER DSCNT AFTER LOSING CABIN PRESSURE.

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AFTER HAVING FLOWN FROM DFW TO SLC; WE CHANGED PLANES AS OUR SCHEDULE DESCRIBED AND WE WERE BRIEFED BY INCOMING CREW CONCERNING MAINT CARRYOVER ITEMS (MCO'S). THIS ACFT HAD AN INOP R AIR CONDITIONING PACK; INOP #2 PRESSURIZATION CTLR; AND AN INOP APU. THE PREVIOUS CREW HAD LOST PRESSURIZATION ON DSCNT ON THE PREVIOUS 2 LEGS; ONCE INTO DEN AND ONCE INTO SLC. SLC MAINT REVIEWED THE RECORDS; CHKED OUT SYS AND REPLACED THE #1 CTLR (ON PRESSURIZATION SYS) BASED ON THEIR FINDINGS AND SIGNED THE ACFT OFF AS AIRWORTHY. WE CHKED THE MEL FOR 1 PRESSURIZATION CTLR OP AND FOUND THE ACFT CAPABLE OF FLYING TO ANY ALT INCLUDING 42000 FT. WE DID NOT CHK THE MEL FOR 1 AIR CONDITIONING PACK INOP; AS THAT CONDITION WAS ON A PREVIOUS MCO. WE WERE DELAYED DUE TO MAINT AND UNABLE TO PERFORM COCKPIT DUTIES UNTIL JUST PRIOR TO PUSHBACK FROM THE GATE BECAUSE MAINT PERSONNEL WERE IN THE COCKPIT REPLACING THE CTLR; FILLING OUT LOGBOOKS; ETC. WE WERE GIVEN THE FLT PLAN AT THE LAST MIN AMONG A FLURRY OF PAPERS (WX; PDC; FUEL SLIP; ACFT WT AND BAL). I LOADED THE FMS ACCORDING TO FLT PLAN WHICH HAD US FILED AT 390. WHILE CLBING OUT OF SLC; THE FO AND I DISCUSSED LEVELING OFF AT 350 BUT COULD FIND NO REF IN OUR PLT OPERATING MANUAL (POM) STATING THAT IT BE NECESSARY TO DO SO ON 1 AIR CONDITIONING PACK (THIS INFO IS NOT IN THE POM). I WAS FLYING THE ACFT AND CONTINUED THE CLB TO 390 (THE DISPATCHED FLT PLANNED ALT). ON LEVEL OFF AT 390; THE CABIN BEGAN TO CLB AT ABOUT 500 FPM. ON MY REQUEST; THE FO CALLED CTR REQUESTING 350. HE MADE 3 ATTEMPTS WITH NO RESPONSE FROM CTR. BY THEN THE CABIN ALT HAD REACHED 10000 FT AND THE WARNING WAS SOUNDING. WE REQUESTED AN EMER DSCNT FROM CTR. STILL NO RESPONSE. AFTER OUR SECOND REQUEST FOR AN EMER DSCNT; ANOTHER AIRLINE CALLED STATING THAT WE HAD AN EMER! CTR THEN RESPONDED TO OUR NEEDS BUT WE WERE ALREADY BEGINNING OUR EMER DSCNT PROCS SQUAWKING 7700. WE HAD AN ONCOMING ACFT BELOW US IN SIGHT AND DELAYED DSCNT UNTIL HE HAD PASSED. THE DSCNT WAS RAPID ENOUGH THAT WE ARRIVED AT 10000 FT MSL BEFORE THE CABIN ALT COULD EXCEED 14000 FT. NO OXYGEN MASKS WERE DEPLOYED IN THE CABIN. WE MADE AN UNSCHEDULED LNDG IN LAS AND PAX WERE SENT ON TO LAX ON ANOTHER ACFT. WE BECAME AWARE IN LAS THAT THE MEL PROHIBITS THE LGT FROM BEING DISPATCHED ABOVE FL350 ON 1 AIR CONDITIONING PACK. HOWEVER; OUR DEPRESSURIZATION WAS CAUSED BY A FAILED EQUIP COOLING VALVE AND WOULD HAVE OCCURRED AT ANY ALT AND WITH BOTH AIR CONDITIONING PACKS OPERATIONAL. THE ACFT IS CAPABLE OF FLT AT FL420 ON 1 AIR CONDITIONING PACK AND WILL MAINTAIN NORMAL PRESSURIZATION WHEN SYS ARE WORKING NORMALLY. IN THIS CASE; OUR ATTN WAS FOCUSED ON THE PRESSURIZATION CTLR AND WE MISSED THE MEL RESTRICTION FOR 1 AIR CONDITIONING PACK OP. OUR DISPATCHER ALSO MISSED IT.