B737-300 CREW DID NOT GET A NEW DISPATCH RELEASE AFTER RETURNING TO THE GATE.

Narrative

UPON CLOSING MAIN ENTRANCE DOOR; THE FLT ATTENDANTS ADVISED US THAT THE DOOR WAS NOT CLOSING PROPERLY. I WENT BACK AND TURNED THE HANDLE AND FOUND IT DIFFICULT TO CLOSE; BUT IT CLOSED AND LOCKED WITH ALL COCKPIT INDICATIONS INDICATING SO. WHEN WE PUSHED BACK AND STARTED THE ENGS; THE FLT ATTENDANTS ADVISED US AGAIN THAT THE DOOR WAS STILL SHOWING SIGNS OF LIGHT THROUGH THE TOP. AT THIS TIME A COMPANY ACFT WAS WAITING FOR THE GATE THAT WE PUSHED OUT OF AND WERE BLOCKING. WE HAD ANOTHER GATE TO GO TO NEXT DOOR; SO WE PROCEEDED TO THAT GATE. I SHUT DOWN BOTH ENGS AND GOT ON THE PHONE WITH MAINT. HE EXPLAINED THAT IN COLD WX; AS WE WERE IN; THE GUIDANCE MECHANISM CAN BE PROBLEMATIC AND WE SHOULD CLOSE THE DOOR SLOWLY. WE DID WHAT HE SAID AND IT CLOSED NORMALLY WITHOUT A PROB. WE PROCEEDED TO PUSH AND TKOF TOWARDS TPA. ENRTE IN MY HASTE I REALIZED THAT I HADN'T OBTAINED ANOTHER RELEASE FROM DISPATCH. AS A NEW CAPT; I'M LEARNING MANY THINGS EVERY DAY. I FEEL THAT BY OUR RUSHING TO VACATE THE GATE FOR COMPANY WAITING BEHIND US; IN ADDITION TO BEING 1 1/2 HRS LATE; I DID NOT THINK OF ALL OF THE ACTIONS I; AS CAPT; WAS TO TAKE. IN THE FUTURE; I WILL KNOW EXACTLY WHAT TO DO AND WON'T BE IN ANY RUSH UNTIL ALL TASKS AND REQUIREMENTS ARE MET.