DC8 CREW FOUND NIL BRAKING AFTER LNDG. ACFT SLID OFF THE END OF THE RWY.

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ILN WX VIA ATIS WAS 310 DEGS AT 11 KTS; 7 OVCST 1 MI -S BROKEN 06/06; ALTIMETER 30.14; TWR WINDS 310 DEGS AT 11 KTS. ON LNDG ROLL; ACFT EXITED THE RWY ONTO THE OVERRUN DUE TO BRAKING ACTION NIL. NO DAMAGE TO ACFT OR RWY LIGHTING. THE APCH TO ILN WAS FLOWN BY FO. APCH WAS STABLE AND ON SPD ALL THE WAY. I CALLED RWY IN SIGHT AT 700 FT AND TOLD HIM TO STAY ON INSTS UNTIL CLOSER TO RWY. TOUCHDOWN WAS IN TOUCHDOWN ZONE AT VREF +5 KTS. SPOILERS AUTOMATICALLY DEPLOYED. AS BRIEFED DURING APCH; I REMINDED HIM TO REVERSE INBOARDS TO MAX CONTINUOUS THRUST; THEN REVERSE #4 SINCE #1 REVERSER WAS INOP. I TOOK CTL AT 100 KTS; ENGS #2; #3; AND #4 WERE IN REVERSE AND I FOUND POOR DECELERATION (BRAKING). DURING LAST 3000 FT; BRAKING ACTION WAS NIL AND FELT LIKE WE ACCELERATED WITH BRAKES FULLY DEPRESSED. WITH #4 ENG COMPRESSOR STALLING; WE EXITED THE RWY INTO THE OVERRUN. WAS ABLE TO MOVE ACFT SLIGHTLY TO L TO AVOID RWY APCH LIGHTING. THE LAST 3000 FT WAS JUST TREATED (TREATMENT UNKNOWN) PRIOR TO MY LNDG. LNDG RWY 22L IS 9000 FT. RWY 22R CLOSED. SUPPLEMENTAL INFO FROM ACN 424984: I WAS FO ON ACR FLT ABCD FROM EWR TO ILN ON JAN/XA/99. THE WX WAS 7 OVCST AND 1 MI VISIBILITY IN SNOW WITH AN 11 KT AND 80 DEG XWIND. THE LONGER RWY; RWY 22R; WAS CLOSED FOR SNOW REMOVAL. (WE LATER LEARNED THAT THE BRAKING ACTION ON THIS RWY HAD RECENTLY BEEN RPTED AS NIL.) WE RECEIVED A BRAKING ACTION RPT OF 'POOR' FROM A PRECEDING DC9. I PERFORMED THE APCH AND LNDG. THE APCH WAS STABLE AND WE TOUCHED DOWN ABOUT 2000 FT DOWN THE RWY. WE USED WHEEL BRAKES; REVERSERS; AND SPOILERS TO SLOW DOWN EFFECTIVELY TO ABOUT 100 KTS. AT THIS SPD AND ABOUT 3500 FT REMAINING; THE CAPT TOOK CTL. THE ACFT THEN SEEMED ALMOST TO ACCELERATE AS OUR RATE OF DECELERATION DECREASED. WITH BRAKES FULLY DEPRESSED; WE SLID OFF THE END OF THE RWY ABOUT 800 FT. WE THEN SHUT DOWN AND CALLED TWR. I THINK IT MIGHT HAVE HELPED TO HAVE A MORE OBJECTIVE BRAKING ACTION RPT THAN THE SUBJECTIVE RPT FROM A SMALLER ACFT. ALSO; HAVE THE OVERALL RPT FOR THE RWY EQUAL TO THE WORSE SEGMENT OF THE RWY.