B737 CREW BEGAN TKOF ON A CLOSED RWY DURING A NIGHT OP.

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WINTER OPS WERE IN EFFECT. AFTER DEICING; TAXIED TO RWY 6R AND HELD SHORT ON TXWY N. TWR SAID; 'CLRED TO CROSS RWY 6R; TURN L HDG 360 DEGS; CLRED FOR TKOF RWY 6L.' I DO NOT RECALL TWR SAYING ANYTHING ABOUT ALSO XING RWY 6C. I CROSSED RWY 6R; TURNED THE CORNER ON THE NEXT RWY AND STARTED THE TKOF ROLL. TWR SAID 'CANCEL TKOF CLRNC; YOU'RE ON RWY 6C.' TKOF WAS REJECTED; I TAXIED CLR AT TXWY S; AND TAXIED TO RWY 6L VIA TXWY G. THE SUBSEQUENT TKOF ON RWY 6L WAS UNEVENTFUL. ALL CHKLISTS WE ACCOMPLISHED. THE FOLLOWING OPERATIONAL THREATS AND DISTRS WERE PRESENT: 1) FIRST WINTER OPS OF THE SEASON: RE-FAMILIARIZATION WITH THE DE-ICE CHKLIST. 2) NIGHT IMC WITH 1 MI VISIBILITY. 3) AFTER PUSHBACK; RWY CHANGE TO SHORTER RWY 6L FROM LONGER RWY 6R; NEW LOAD MANIFEST. SUPPLEMENTAL INFO FROM ACN 622371: CONTRIBUTING FACTORS AND THREATS WOULD BE 'FLT CTL' ON THE ANNUNCIATOR. WHILE I WAS RUNNING THE BEFORE TKOF CHKLIST AND LOOKING UP TO RESET THE YAW DAMPER; VISIBILITY 1 MI; RWY MARKINGS AND NUMBERS COVERED BY PREVIOUS BLOWING SNOW; SOME RESIDUAL DEICE FLUID ON WINDSHIELD; TXWYS AND RWYS SNOW COVERED; NIGHTTIME; AND RWY 6L BEING FAIRLY NEW. THIS EVENT TO ME IS ABOUT AS CLASSIC AS AN EVENT COULD BE WHEN IT COMES TO SHOWING HOW IMPORTANT VIGILANCE AND MONITORING IS. THIS IS AN EVENT I SHALL NEVER FORGET; AND THE IMPORTANCE OF ALWAYS SHIFTING MY ATTN OUTSIDE THE COCKPIT AS WELL AS WITHIN; SHALL NEVER BE UNDERESTIMATED.