A FOKKER 100 WAS DISPATCHED IN NON COMPLIANCE WITH THE AFT ELECTRONICS DOOR PARTIALLY OPEN CAUSING LOSS OF PRESSURIZATION. NO EMER OR DIVERSION.

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THE ACFT WOULD NOT PRESSURIZE AFTER TKOF. WE LEVELED AT 9000 FT TO INVESTIGATE THE PROB. WE FOUND THAT BOTH AUTO AND MANUAL PRESSURIZATION DID NOT WORK. HOWEVER; CABIN TEMP CTL DID FUNCTION. WE ASKED FOR DELAYING VECTORS TO STAY CLOSE TO ZZZ UNTIL I HAD A CHANCE TO CONFER WITH DISPATCH CONCERNING FUEL AND WX PLANNING. I ASKED DISPATCH TO RUN THE NUMBERS FOR 10000 FT CRUISE FROM ZZZ TO ZZZ1. AFTER I DETERMINED THAT FUEL AND WX REQUIREMENTS WOULD BE MET ALLOWING FOR A SAFE FLT TO ZZZ1 WE SECURED A NEW CLRNC AT 10000 FT WITH A RTE ZZZ-ZZZ2-ZZZ1. WE HAD A CLOSE CONNECTION FOR OUR NEXT FLT TO ZZZ3 SO I WENT TO THE NEW GATE TO START FLT PLANNING. AFTER I LEFT; A MAINT SUPVR INFORMED THE COPLT THAT THEY HAD FOUND THE AFT AVIONICS HATCH OPEN. THE COPLT THEN CHKED THE HATCH AND OBSERVED THE DOOR UNLOCKED AND OPEN ABOUT 2 INCHES. DURING PREFLT AT ZZZ THE COPLT CONFIRMED THAT THE AFT AVIONICS HATCH DOOR WAS OPEN. PRECONDITIONED AIR WAS HOOKED UP AND ONE OF THE AVIONICS DOORS IS SUPPOSED TO BE OPENED. IF THE AGENT CLOSES THE FORWARD ENTRY DOOR FOR DEP AND THE AVIONICS HATCH IS NOT OPEN; THE PRECONDITIONED AIR WILL CREATE A VERY AGGRESSIVE PRESSURE BUMP CAUSING EXTREME DISCOMFORT TO THE PAX AND CREW. ALSO; THERE IS SOME RISK TO THE AGENT THAT THE FORWARD ENTRY DOOR COULD FORCEFULLY REOPEN. FOR THESE REASONS THE AVIONICS HATCH IS SUPPOSED TO BE OPEN UNTIL THE PRECONDITIONED AIR IS DISCONNECTED. THE DOOR LIGHTS WERE IN FACT OUT PRIOR TO BRAKE RELEASE AND PUSH AT ZZZ. THE DOOR LIGHTS WERE OUT FOR TKOF. THE DOOR LIGHTS WERE OUT DURING CLB; CRUISE; DSCNT; AND TAXI IN. AFTER PARKING THE 3 CARGO DOOR LIGHTS AND THE FORWARD ENTRY DOOR LIGHT CAME ON AS THE GND CREW AND AGENT OPENED THE DOORS. I DON'T RECALL THE AFT AVIONICS HATCH LIGHT COMING ON EVEN AFTER PARKING AT ZZZ1. WHILE RUNNING OUR CHKLIST FOR OUR NEXT FLT; TO ZZZ3; CHIEF PLT CAME IN THE COCKPIT AND SAID THAT HE HEARD THAT I HAD TAKEN OFF OUT OF ZZZ WITH A DOOR OPEN AND CONTINUED TO ORD UNPRESSURIZED. OBVIOUSLY CHIEF PLT WAS CONCERNED ABOUT THIS IRREGULAR OP OF FLT ZZZ TO ZZZ1. I STOPPED THE CHKLIST AND ANSWERED HIS QUESTIONS TO THE BEST OF MY ABILITY. THE REASON FOR THIS AND SAFETY RPT IS TO PROVIDE SUPPORTING DETAIL CONCERNING OUR PRESSURIZATION ABNORMAL AND MY DECISION TO CONTINUE TO ZZZ1. SINCE THERE WAS NO ADVERSE IMPACT TO THE PAX AND I DID NOT NEED TO DECLARE AN EMER I DO NOT PLAN FURTHER RPTING TO THE FAA.