A B737-700 ON CLBOUT AT 7000 FT HAS CABIN ATTENDANT RPT OF LOUD NOISE FROM 1L DOOR. UNABLE TO PRESSURIZE CABIN DIVERTS TO SUITABLE ARPT.

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ON CLBOUT; FLT ATTENDANT CALLS AND COMPLAINS ABOUT A LOUD AIR NOISE COMING FROM AROUND THE FORWARD ENTRANCE DOOR. WE LOOKED UP AT THE OVERHEAD PANEL. THERE WAS NO DOOR LIGHT; BUT THE ACFT WAS NOT PRESSURIZING NORMALLY. WE LEVELED OFF AT 10000 FT. FO WAS FLYING. AT THIS TIME THE FLT ATTENDANT CALLS BACK AND SAYS SHE CAN FEEL AIR COMING AROUND THE DOOR. THE ACFT WAS PRESSURIZED ONLY TO 7000 FT. CAPT PULLS OUT QRH AND READS LOSS OF PRESSURIZATION CHKLIST. AT FIRST WE THOUGHT WE JUST HAD A BAD DOOR SEAL. THE CAPT DECIDES TO TAKE A LOOK. HE NOTICES THE DOOR IS NOT SEALED ON THE L SIDE. ALL ATTEMPTS TO CLOSE THE DOOR FULLY FAIL. WHEN THE CAPT CAME BACK HE PERFORMED THE DOOR ANNUNCIATOR CHKLIST EVEN THOUGH WE DID NOT HAVE A LIGHT. IT WAS NOW TIME TO LAND AT A SUITABLE ARPT. BY THIS TIME WE WERE CLOSER TO ZZZ2; BUT OUR RADAR SHOWED BAD WX IN THAT AREA. WHILE I FLY AND TALK ON #1 RADIO; THE CAPT ATTEMPTS TO CALL DISPATCH. DISPATCH CONFIRMS THE BAD WX IN ZZZ2; BY THIS TIME WE WERE ALREADY PAST IT; SO WE CONTINUED TO ZZZ. COM WITH THE FLT ATTENDANTS AND PAX WAS KEPT UP WITH. WE DID NOT DECLARE AN EMER. THE QUESTION IS; 'SHOULD WE HAVE TURNED BACK TO ZZZ1 WHEN WE WERE ABEAM ZZZ2 OR CONTINUE TO ZZZ? OR; SHOULD WE HAVE NOT MESSED WITH ANY OF THE ABOVE AND JUST TURNED AROUND WHEN FIRST NOTIFIED?' WE WANTED TO ASSESS THE PROB FULLY SO WE DID. THERE WAS NO REASON TO RUSH. WE WERE SAFE AND SOUND AT 10000 FT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE PAX AGENT AT THE DEP STATION MAY HAVE NOT CLOSED THE DOOR CORRECTLY BUT AT NO TIME DID THE DOOR WARNING LIGHT ILLUMINATE. THE RPTR SAID AT THE DIVERSION STATION THE TECHNICIANS BELIEVED THE DOOR WAS FALSE LATCHED AND ADJUSTED THE STOPS AND THE DOOR OPERATED NORMALLY.