MD80 FLT CREW DURING PUSHBACK FOR START HAS A MISCOM WITH THE RAMP PUSHBACK CREW. COM IS NOT PROPERLY ESTABLISHED; THE TOW BAR IS DISCONNECTED; THE ACFT ROLLS FORWARD PRIOR TO BRAKES BEING SET.

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DURING PUSHBACK; DISCOVERED THAT APU WOULD NOT DELIVER AIR FOR ENG START. CAPT PARKED BRAKES AND INSTRUCTED CREW TO REMAIN CONNECTED WHILE WE WERE TROUBLESHOOTING; BUT THEY DISCONNECTED ANYWAY. SEVERAL MINS ELAPSED WHILE WE CARRIED ON RADIO COM WITH RAMP AND MAINT ABOUT THE PROB. EVERYONE WAS IN FAVOR OF TOWING BACK TO THE GATE; BUT THE GND CREW REFUSED TO HOOK UP -- THEY SAID THAT SOME RAMP AGENTS HAD GONE ON BREAK; AND THE AVAILABLE AGENTS WERE NOT COMFORTABLE WITH TOWING THE AIRPLANE IN -- THEY ONLY KNEW HOW TO PUSH IT OUT. THE SITUATION WAS CHAOTIC; WITH SOME RAMP CONVERSATION CARRIED OUT THROUGH OPEN COCKPIT WINDOWS. AT SOME POINT THE TUG AND TOW BAR WAS RECONNECTED; AND PARKING BRAKES RELEASED; IN PREPARATION FOR TOWING BACK TO GATE. SUDDENLY THE CAPT REALIZED THAT AIR WAS AVAILABLE FROM THE APU -- THE PROB FIXED ITSELF -- CALLED THE AVAILABLE RAMP CREW TO THE ACFT TO DISCONNECT. THE RAMP CREW DID NOT ESTABLISH COMS; AND DECIDED TO DISCONNECT THE TUG AND TOW BAR ON THEIR OWN AUTH. I WAS NOT AWARE THAT THE BRAKES WERE NOT PARKED. AFTER THE FIRST ENG START WAS COMPLETE; I NOTICED THE AIRPLANE WAS ROLLING FORWARD; SO I IMMEDIATELY STEPPED ON THE BRAKES. IT APPEARED THE GND CREW HAD JUMPED CLR -- THE AIRPLANE DIDN'T MOVE MORE THAN A COUPLE OF FT. WHILE THE CIRCUMSTANCES THAT LED TO THIS WERE UNUSUAL; THERE ARE SOME CLR WEAKNESSES IN OUR PROCS AND PROTOCOL THAT CONTRIBUTED TO THE EVENT. FIST; THE FINAL 'START/PUSH' ITEMS ON THE CHKLIST DO NOT HAVE ANY REF TO THE PARKING BRAKE; SO THERE IS NO BACKSTOP FOR MEMORY ON THIS IMPORTANT ITEM -- THE PARKING BRAKE ITEM IS IN THE WRONG PLACE ON THE CHKLIST. SECONDLY; THE COCKPIT PROTOCOL DOES NOT KEEP THE FO SUFFICIENTLY IN THE LOOP REGARDING ALL START-RELATED ACTIVITY -- LIKE THE PARKING BRAKE. THIRD; THE CAPT DID NOT CALL FOR ANY CHKLIST BEFORE START BECAUSE THE 'BEFORE START' CHKLIST HAD ALREADY BEEN COMPLETED.