What was found
CABIN PRESSURIZATION CONTROL NOT PRESSURIZING - PRESSURIZATION QUIT WORKING AS WE CLIMBED TO A HIGHER ALTITUDE. GOING THROUGH 31,500 FEET I FELT THAT THE CABIN PRESSURE DIDN'T FEEL RIGHT. I LOOKED AND THE CABIN WAS AROUND 7,000 FEET, CLIMBING AT 1000 FEET PER MINUTE WITH A DIFFERENTIAL OF 7 PSI. WE STOPPED OUR CLIMB AT 32,000 FEET AND THE CABIN CONTINUED TO CLIMB SLOWLY. WE ASKED FOR FL200 AND GOT CLEARANCE. AS WE DESCENDED TO FL200 THE CABIN ALTITUDE LIGHT CAME ON. WE RAN THE CHECKLIST AND DECLARED AN EMERGENCY. CABIN ALTITUDE NEVER GOT ABOVE 12,500. AS WE GOT BELOW 10,000 MSL FEET THE CABIN ALTITUDE CONTINUED DESCENDING.