LGT CAPT FORGOT TO TURN ON THE SEATBELT SIGN BEFORE PUSHBACK.

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FAILED TO TURN ON SEATBELT SIGN PRIOR TO PUSHBACK. SEATBELT SIGN REMAINED OFF UNTIL DISCOVERED AT 10000 FT MSL DURING CLB TO ALT. ENTIRE ACTION DONE INADVERTENTLY. BECAME DISTR PRIOR TO PUSHBACK (6 REASONS): 1) FLT OVER AN HR LATE. MAINT ISSUE WITH ORIGINAL ACFT; RESULTING IN ACFT SWAP. 2) LINE MAINT MEL'ED FLT/GND SVC INTERPHONE JUST PRIOR TO PUSHBACK. 3) OPPORTUNITY TO BRIEF PUSHBACK CREW DID NOT PRESENT ITSELF UNTIL AFTER L-1 DOOR CLOSED AND JETWAY TAKEN AWAY. I NEVER DISCOVERED WHO THE PUSHBACK CREW WAS UNTIL 10 MINS AFTER L-1 DOOR CLOSED AND JETWAY REMOVED. (THEY WERE BUSY WITH RAMP DUTIES.) 4) FLT DEST REQUIRED ADDITIONAL PAX ANNOUNCEMENTS/BRIEFINGS. THIS TOOK UP ADDITIONAL TIME AND ADDED TO THE DISTR. 5) CONTINUAL DISTRS FROM THE CUSTOMER SVC AGENT TO SHUT THE L-1 DOOR AND REMOVE THE JETWAY BEFORE WE WERE READY. 6) PRIOR TO PUSH; THE ONLY WAY I COULD COMMUNICATE WITH CONTRACT GND CREW WAS THROUGH THE OPEN L SLIDING WINDOW. THIS PRESENTED A PROB WITH THE LOUD NOISE OF RAMP OPS; LANGUAGE DIFFICULTY; AND GND CREW UNFAMILIAR WITH PROPER PROCS. THESE ITEMS HAD TO BE RESOLVED PRIOR TO PUSHBACK. THE FLT CREW ACCOMPLISHED (RAN) THE 'PRIOR TO PUSH' CHKLIST AND I ABSOLUTELY BELIEVED I PLACED THE SEATBELT SIGN ON PRIOR TO PUSH; BUT NOW REALIZE THAT I WAS DISTR WITH ALL THE ABNORMAL OPS AND OMITTED TURNING IT ON UNTIL 10000 FT. 2 LESSONS LEARNED: 1) DELIBERATELY ACCOMPLISH CHKLIST ITEMS; PARTICULARLY WHEN DISTRS EXIST. OBSERVE AND DOUBLECHK EACH ITEM. 2) IN THE FUTURE; I WILL INSTRUCT THE CUSTOMER SVC AGENT TO BRING THE PUSHBACK CREW TO THE COCKPIT FOR PROPER BRIEFING WHENEVER I HAVE A SIMILAR SIT WITH AN MEL'ED FLT/GND SVC INTERPHONE INOP.