A B737-800 FLT CREW INADVERTENTLY SLID DURING TKOF ROLL FROM RWY 1R AT MCI; RESULTING IN AN ABORTED TKOF AND ENDING WITH THE ACFT NOSEWHEEL LEAVING THE RWY.

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FO WAS THE PF. HE LOADED THE FMS AND I PERFORMED THE EXTERIOR PREFLT. THE ACFT WAS FOUND TO BE NORMAL AND I OBSERVED THAT THE SNOW FLURRIES WERE VERY LIGHT. THE FLT PUSHED ON SCHEDULE AND BOTH ENGS WERE STARTED FOR THE TAXI ON THE SNOW COVERED TXWYS AND APPROPRIATE CHKLISTS WERE COMPLETED. THE TXWYS NEXT TO RAMP WERE MOSTLY CLR BUT THE REST WERE SNOW COVERED. FO CALLED FOR AND RECEIVED TAXI CLRNC AND WE WERE ASSIGNED RWY 1R. DURING THE TAXI TO THE RWY; MY TAXI SPD WAS KEPT SLOW BECAUSE OF TXWY CONDITIONS. THE LOWERING OF FLAPS AND THE TAXI CHKLIST WERE DELAYED UNTIL APPROX 100 YARDS FROM THE HOLD SHORT. AT THAT POINT THE FLAPS WERE LOWERED AND TAXI CHKLIST COMPLETED. WE WERE INSTRUCTED TO HOLD SHORT FOR LNDG TFC. THE FO MADE THE PA FOR FLT ATTENDANTS TO PREPARE THE CABIN AND WE COMPLETED THE BEFORE TKOF CHKLIST DOWN TO THE FINAL ITEMS. I OBSERVED THE WINDSOCK AT THIS POINT AND IT WAS APPROX 45-50 DEGS OFF RWY HDG APPROXIMATING ATIS READINGS. WHEN THE ACFT LANDED; TWR GAVE US CLRNC TO POS AND HOLD. I TAXIED THE ACFT INTO POS AND HOLD AND WE COMPLETED THE CHKLIST DOWN TO EXTERIOR LIGHTS. AT THIS POINT I GAVE CTL OF THE ACFT TO FO. TWR GAVE US CLRNC FOR TKOF AND WE FINISHED THE BEFORE TKOF CHKLIST. FO STARTED ADDING PWR. AT THIS POINT I MADE A SCAN OF THE COCKPIT INSTS; WITH EVERYTHING BEING NORMAL. AS MY SCAN CAME BACK TO THE OUTSIDE; I SAW THE ACFT MOVING AWAY FROM CTRLINE AND TOWARDS THE R SIDE OF THE RWY. FO ALREADY WAS BRINGING THE THRUST LEVERS TO IDLE. AT THE SAME TIME; I ALSO GOT ON THE THRUST LEVERS TO ADD REVERSE THRUST AND ALSO GOT ON THE BRAKES; BUT THE ACFT CONTINUED TO SLIDE TOWARD THE R SIDE OF THE RWY. I ALSO GOT ON THE NOSEWHEEL STEERING AND WENT FULL L. THE ACFT TRAVELED ABOUT 200 FT FROM WHERE THE TKOF HAD STARTED AND THE NOSEWHEEL CAME TO REST OFF THE PREPARED SURFACE. THE ENGS WERE BROUGHT TO IDLE JUST BEFORE THE ACFT CAME TO A STOP. FO MADE THE CALL TO THE TWR TO ADVISE THEM OF THE SIT. THE PA WAS MADE TO HAVE PAX REMAIN SEATED. I DECIDED TO START THE APU AND SHUT DOWN THE ENGS. FROM THIS POINT I HANDLED THE COM WITH THE PAX AND THE FLT ATTENDANTS AND FO MADE THE CALLS TO TWR. PA'S WERE MADE EVERY 2-4 MINS ON THE PROGRESS OF THE BUSSES. PAX REMAINED CALM THROUGHOUT. I DECIDED TO SEND THE FLT ATTENDANTS ON THE BUSSES WITH THE PAX. WE TRIED TO CONTACT COMPANY OPS BUT NO LUCK. I WAS ABLE TO CALL THE DISPATCHER AND INFORM HIM OF OUR SIT AND WE DECIDED WE WOULD HAVE TO BUS THE PAX BACK TO THE TERMINAL. OUR DISPATCHER AND COMPANY OPS ARRANGED FOR THE AIR STAIRS AND BUSSES TO BE ESCORTED TO OUR ACFT. WE COMPLETED THE AFTER LNDG AND SHUTDOWN CHKLISTS EXCEPT ANTI-COLLISION LIGHT. THE PAX WERE DEPLANED VIA THE 2L DOOR AND AIR STAIRS ONTO 5-6 BUSSES. WE ELECTED TO STAY BEHIND FOR A FEW MINS TO MAKE SURE THAT THE BAGS AND ACFT WOULD BE TAKEN CARE OF. WE LEFT THE ACFT APU RUNNING AND IN THE HANDS OF QUALIFIED PERSONNEL. WE WERE GIVEN A RIDE TO COMPANY OPS BY ARPT OPS PERSONNEL. SUPPLEMENTAL INFO FROM ACN 607546: CONDITIONS WERE LIGHT SNOW; WIND FROM THE N AT 11 KTS. RWY 1L WAS CLOSED AND WE LANDED ON RWY 1R. WE RPTED THE BRAKING ACTION AS FAIR. WE RECEIVED CLRNC TO TAKE OFF; LIGHTS WERE TURNED ON AND THE BEFORE TKOF CHKLIST WAS CALLED COMPLETE. I ADDED PWR TO APPROX 35% N1. THE ENGS SPOOLED UP NORMALLY AND THE ACFT BEGAN TO MOVE FORWARD. I THEN SELECTED TOGA. I WATCHED THE PWR COME UP AND AT ABOUT 80% N1; I SAW THAT WE WERE DRIFTING SIDEWAYS TO THE R. I ATTEMPTED TO CTL DIRECTION WITH THE RUDDER PEDALS. WE CONTINUED IN A R DRIFT. I PULLED THE PWR BACK AND ATTEMPTED BRAKING TO NO AVAIL. WE TRIED REVERSING THE ENGS BUT THE ACFT CONTINUED MOVING TO THE R.