A B737-300 WAS DISPATCHED WITH THE E&E COMPARTMENT DOOR CLOSED BUT NOT LOCKED CAUSING THE CABIN TO NOT PRESSURIZE ON TKOF.

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ACFT WAS LOADED AND JETWAY PULLED BACK. CALLED FOR BEFORE PUSH CHKLIST. NOTICED 2 LIGHTS ILLUMINATED: EQUIP AND CARGO DOOR LIGHTS. CARGO DOOR LIGHT EXTINGUISHED SHORTLY THEREAFTER AND TOLD GND PERSONNEL ABOUT EQUIP DOOR LIGHT. GND PERSONNEL ADVISED ME THAT ALL ACCESS PANELS AND DOORS WERE CLOSED. THEY OPENED THE EQUIP DOOR SEVERAL TIMES AND CLOSED IT AGAIN. IT APPEARED TO BE A SWITCH PROB. I WAS ASSURED AGAIN THAT EVERYTHING WAS CLOSED UP. THIS WAS A CONTRACT MAINT STATION AND IT WOULD HAVE FURTHER DELAYED THE FLT TO CALL THEM OUT. I FELT I HAD DONE EVERYTHING NECESSARY UNDER THE CIRCUMSTANCES SO WE PUSHED BACK AND DURING THE TKOF THE ACFT WOULD NOT PRESSURIZE. THERE WAS CONSIDERABLE NOISE AS IF A DOOR BELOW THE COCKPIT HAD OPENED. WE KEPT A CLOSE PATTERN AND MADE AN UNEVENTFUL VISUAL APCH AND LNDG. I ASKED THE OPS PERSONNEL TO CALL CONTRACT MAINT. I WAS INFORMED BY THE MAINT MAN THAT THE DOOR WAS INDEED OPEN. HE CLOSED IT AND WE CONTINUED. IT SEEMS THERE WAS NOTHING WRONG WITH THE LIGHT AND THERE MUST BE 2 DOORS ON THE LIGHT. THE PUSH CREW DID NOT NOTICE THE OTHER DOOR. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE GND PERSONNEL ONLY CHKED THE FORWARD RADAR COMPARTMENT DOOR BUT IGNORED THE ELECTRONIC AND ELECTRICAL COMPARTMENT DOOR AFT OF THE NOSE GEAR. THE RPTR SAID BOTH DOORS CTL ONE WARNING LIGHT BUT ONLY ONE WAS OPENED AND CLOSED. THE RPTR SAID ON RETURN TO THE GATE THE CONTRACT MECH FOUND THE ELECTRONIC AND ELECTRICAL COMPARTMENT DOOR CLOSED BUT NOT LOCKED.