As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AT ABOUT FL 340 CLIMBING TO 350 WE HAD THE RED CABIN ALTITUDE WARNING LIGHT AND AURAL WARNING COME ON. WE IMMRDIATELY DONNED OUR OXYGEN MASKS AND CO PILOT STARTED THE CABIN ALTITUDE EMERGENCY CHECKLIST. ONCE CREW COMMUNICATION WAS ESTABLISHED WE SQUAWKED 7700 AND NOTIFIED ATC THAT WE WERE HAVING CABIN PRESSURIZATION ISSUES AND NEEDED TO DESCEND AND RETURN TO OUR DEPARTURE (HOME BASE) AIRPORT. DURING THE DESCENT WE WERE ABLE TO REESTABLISH PRESSURIZATION CONTROL THROUGH MANUAL MODES, APPROACH AND LANDING WERE MADE NOEMALLY WITHOUT INCIDENT.