B737-300 CREW WAS ALERTED BY THE CABIN ALT WARNING THAT THE CABIN EXCEEDED 10000 FT. UNABLE TO TALK TO THE RADAR CTLR; THEY BEGAN AN EMER DSCNT WITHOUT CLRNC AND THEY DIVERTED TO AN ALTERNATE ARPT FOR MAINT. EMER NOT DECLARED.

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WE WERE CRUISING AT 35000 FT WHEN THE CABIN ALT WARNING HORN SOUNDED. WE CONFIRMED THAT THE CABIN ALT WAS ABOVE 10000 FT AND DONNED OUR OXYGEN MASKS. WE DID NOT HAVE ANY WARNING ANNUNCIATOR LIGHTS. I TURNED THE PRESSURIZATION SELECTOR TO STANDBY; ATTEMPTING TO REGAIN CTL OF THE CABIN. WHEN THAT DID NOT WORK; I TRIED THE MANUAL AC AND THEN MANUAL DC; BUT THAT DID NOT WORK EITHER. THE DECISION WAS MADE TO START A DSCNT. THE CTLR WAS TALKING TO OTHER TFC AND WE COULD NOT GET A WORD IN TO ADVISE OF OUR PROB. FINALLY WE HAD A BREAK AND ADVISED OF OUR DSCNT AND ASKED FOR THE MINIMUM VECTORING ALT. IT TOOK HIM A FEW MINS TO RESPOND WITH THE ALT. BY THIS TIME; THE CABIN PRESSURIZATION STARTED TO RECAPTURE; DSNDING WITH THE ACFT. WE HAD ALREADY DSNDED TO AROUND 25000 FT. THE CTLR THEN ASKED IF WE WOULD LIKE TO DECLARE AN EMER; AND SINCE THINGS WERE THEN UNDER CTL; WE DECLINED. DURING THE DSCNT; WE RAN ALL APPLICABLE CHKLISTS. AFTER SPEAKING WITH THE COMPANY AND SINCE WE WERE NOT SURE OF WHAT HAD CAUSED THE FAILURE; THE DECISION WAS MADE TO DIVERT TO MCI. WE CHKED FOR OVERWT LNDG DATA. AN UNEVENTFUL; ALTHOUGH OVER MAX LNDG WT LNDG WAS MADE. ALTHOUGH WE DSNDED OUT OF ALT WITHOUT CLRNC; I FEEL IT WAS THE APPROPRIATE ACTION TO TAKE. LOOKING BACK; IT MIGHT HAVE BEEN MORE APPROPRIATE TO DECLARE AN EMER IMMEDIATELY WHEN WE FIRST SPOKE WITH THE CTLR ABOUT THE DSCNT AND THEN CANCELLED IT LATER ONCE THE PROB WAS CTLED.