A DC9-40 WAS DISPATCHED IN NON COMPLIANCE WITH THE AFT CARGO DOOR OPEN AND THE AFT CARGO DOOR WARNING LIGHT INOP.

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ACFT DID NOT PRESSURIZE AFTER DEP. LEVELED OFF AT 7000 FT AND PERFORMED COMPANY OPS MANUAL PROC; WHICH DID NOT WORK. WE HAD GOOD AIR CONDITIONING PRESSURE FROM BOTH PACKS AND MANUALLY CLOSED OUTFLOW VALVE. ALL DOOR ANNUNCIATOR LIGHTS TESTED PROPERLY AND INDICATED OUT/CLOSED. CALLED DISPATCH AND MAINT CTL ON RADIO FOR ADDITIONAL ASSISTANCE. WE HAD PLENTY OF FUEL AND UNDER THE DIRECTION OF DISPATCH AND MAINT CTL; CONTINUED TO MSP WITH NEW FUEL BURN/TIME NUMBERS. JUST PASSED 1/2 OF FLT; LEAD FLT ATTENDANT RPTED WIND NOISE IN AFT CABIN AND FLOOR COLD IN AFT CABIN. AFT CARGO DOOR FOUND FULLY OPEN BY MAINT CTL PERSONNEL ON ARR IN MSP. ANNUNCIATOR LIGHTS STILL TESTED PROPERLY AND INDICATED THE DOOR WAS CLOSED. MAINT FOUND A BAD SENSOR PLUG. IT WAS MEL'ED IN MSP. NOTE: WE TAXIED IN FRONT RWY 12L TO MSP GATE XA WITH NO ONE NOTICING DOOR OPEN; AND DEPARTED BISMARCK; ND; WITHOUT TWR OR ANYONE ELSE NOTICING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE DOOR WARNING SYS WORKED OK INBOUND TO BIS. THE RPTR SAID THE DOOR WAS DISCOVERED OPEN WHEN THE ACFT ARRIVED AT MSP AND MAINT DISCOVERED THE DOOR SENSOR CONNECTOR DAMAGED. THE RPTR STATED IT WAS A MILLION TO ONE ODDS HAVING A HUMAN AND MECHANICAL FAILURE ON THE SAME COMPONENT SIMULTANEOUSLY.