FLT CREW OF B734 FAIL TO PROPERLY DOCUMENT A FAILED IGNITION SYS DISCOVERED ON ENG START.

Narrative

AFTER PUSHBACK ON ENG START: START ENG #1; NO EGT RISE WITHIN 10 SECONDS AFTER START LEVER RAISED TO IDLE. START LEVER PLACED TO CUTOFF PER ABORTED START CHKLIST. AFTER ABOUT 1 MIN; START SWITCH TO OFF. ENG WOUND DOWN TO ZERO. ENG IGNITION SWITCHED FROM 'IGNITION L' TO IGNITION R.' ATTEMPTED ANOTHER START AND #1 THEN #2 ENGS STARTED NORMALLY. TAXIED; TOOK OFF; REALIZED MY MISTAKE. I SHOULD HAVE RETURNED TO THE GATE FOR AN MEL. THAT THOUGHT DID NOT CROSS MY MIND UNTIL PASSING 10000 FT ON CLBOUT. MY THINKING ON THE GND WAS SOMETHING ALONG THESE LINES: R IGNITION WORKS; ENGS STARTED NORMALLY; PROB SOLVED; PRESS ON. WE LOOKED UP THE MEL AFTER LEVELOFF AND UNDERSTOOD AN INFLT MEL WAS NOT AN OPTION. WE ALSO DUG THROUGH THE LOGBOOK TO FIND THIS WAS A REPEAT WRITE-UP. I CHOSE TO CONTINUE THE FLT TO DEST AND PUT THE APPROPRIATE WRITE-UP IN THE ACFT LOGBOOK. AFTER LNDG I CONTACTED THE DUTY MGR AND DISPATCH VIA TELEPHONE TO INFORM THEM OF THE SIT AND THE MAINT WRITE-UP I PLACED IN THE LOGBOOK. SUPPLEMENTAL INFO FROM ACN 596644: I HAD BEEN JUST FINISHING UP COPYING THE TKOF DATA AND SETTING IT IN THE FMC WHEN THE FO TRIED TO START THE #1 ENG THE FIRST TIME. WHEN HE SAID THERE WAS A PROB WITH THE START; I WASN'T SURE WHAT INDICATIONS HE HAD; WHICH IS WHY I RESET THE BLEED VALVES AND ISOLATION VALVE TO MAKE SURE WE WERE GETTING ENOUGH AIR TO THE ENG. AT NO TIME DID EITHER ONE OF US KNOWINGLY FORGET TO DEAL WITH THE FAULT. IT WAS NOT UNTIL CLBING OUT ABOVE 10000 FT DID FO BRING UP THAT WE STILL HAD A PROB. BOTH OF US FELT LIKE THE 'DOLTS' THAT WE WERE AND DISCUSSED THE BEST COURSE OF ACTION. I AM EXTREMELY SORRY I DID NOT HELP RECOGNIZE THE PROB AND I FEEL EQUALLY RESPONSIBLE FOR THE OUTCOME.