FA20 ENCOUNTERS SLICK RWY AT SRB RESULTING IN RWY EXCURSION.

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ILS RWY 4 (SRB); CAPT FLYING. WX: 900 FT BROKEN; 1500 FT BROKEN; 2100 FT OVCST; 7 MI VISIBILITY; TEMP/DEWPOINT MISSING; WIND 220 DEGS AT 7 KTS ALTIMETER 29.77. LNDG WT 23000 LBS. VREF 122 KTS. ANTISKID WAS CHKED PRIOR TO LNDG. APPLIED AIR BRAKES UPON TOUCHDOWN. WET RWY; NOSE GEAR WAS PUT ON RWY. BRAKES WERE APPLIED/ANTISKID WAS WORKING (WE BOTH FELT THE 'JERKY MOTION'). DECELERATION WAS NORMAL. FO CALLED 100 KTS. FO CALLED 80 KTS/HANDS OFF AIR BRAKE (PER SOP). AT APPROX 75 KTS; CAPT DID NOT FEEL ANY BRAKING ACTION; WITH NO DECELERATION. WENT TO BRAKES II (WITHOUT ANTISKID) WITH SAME RESULTS -- NO BRAKING ACTION; AND SO ELECTED PARKING BRAKE (WITH APPROX 1000 FT LEFT). ALSO; PARKING BRAKE DIDN'T GIVE ANY BRAKING ACTION. MAINTAINED DIRECTIONAL CTL AND SLID OFF THE END OF THE RWY. FOLLOWED BY SHUTDOWN CHKLIST. NEXT MORNING; FAA REPRESENTATIVE WITH OUR COMPANY MAINT TEAM INSPECTED THE RWY AND IDENTED LNDG POINT; BRAKE TRACK WITH ANTISKID AND BRAKE TRACK WITHOUT ANTISKID. THEY ALSO NOTED THAT THE RWY SURFACE WAS MADE OUT OF BLACKTOP ASPHALT WITH APPARENT SEAL COATING CREATING A VERY SLICK SURFACE.