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

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ACFT DID NOT PRESSURIZE AFTER DEP. LEVELED OFF AT 7000 FT AND PERFORMED COMPANY OPERATING MANUAL PROCS; WHICH DID NOT WORK. HAD GOOD AIR CONDITIONING PRESSURE FROM BOTH PACKS AND MANUALLY CLOSED OUTFLOW VALVE. ALL DOOR ANNUNCIATOR LIGHTS TESTED PROPERLY AND INDICATED CLOSED (LIGHTS OUT). CALLED COMPANY DISPATCH/MAINT CTL ON RADIO FOR MORE ASSISTANCE. AGREED TO CONTINUE TO MSP SINCE WE HAD PLENTY OF FUEL; WITH NEW FUEL CONSUMPTION NUMBERS. JUST PAST 1/2 WAY TO MSP; LEAD FLT ATTENDANT RPTED LOTS OF WIND NOISE IN AFT CABIN AND FLOOR WAS COLD IN AFT CABIN. LANDED IN MSP WITH NO PROBS. AFT CARGO DOOR FOUND FULLY OPEN BY MAINT CTL PERSONNEL UPON ARR AT GATE. ANNUNCIATOR LIGHTS STILL TESTED PROPERLY AND INDICATED CLOSED. BAD DOOR SENSOR PLUG. MEL'ED ITEM IN MSP. DID NOT LOSE ANY BAGGAGE ACCORDING TO GND SVC. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE CONDITION THE DOOR WAS FOUND ON ARR AT MSP WAS CARGO DOOR FULLY OPEN AND THE CARGO NET INSTALLED. THE RPTR SAID THE DOOR WARNING STILL TESTED OK ON THE GND AT MSP. THE RPTR SAID MAINT FOUND A DEFECTIVE CONNECTOR ON THE DOOR SENSOR WHICH WAS DEFERRED AS NO PARTS WERE AVAILABLE AT MSP.