ACR LGT FLC EXPERIENCES RWY EXCURSION AFTER LONG AND FAST TOUCHDOWN AND FAILURE OF REVERSERS DUE AIR GND SWITCH LOGIC DISCREPANCY.

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GIVEN 'SLAM-DUNK' VISUAL APCH TO RWY 04R AT ORD BY CHICAGO APCH CTL. RESULTED IN STEEP FAST FINAL APCH. WE WERE INSTRUCTED BY TWR TO 'ROLL TO THE END.' TOUCHED DOWN ABOUT 2000 DOWN RWY AND IMMEDIATELY PULLED THRUST REVERSE LEVERS TO INTERLOCK POS. AFTER SEVERAL VIGOROUS AND UNSUCCESSFUL ATTEMPTS TO RAISE REVERSE LEVERS OUT OF REVERSE IDLE -- ADVISED CAPT THAT REVERSE LEVERS WERE STUCK. NEXT; AFTER MANUAL BRAKING WAS APPLIED; GENTLY AT FIRST THEN MAX EFFORT WHEN BRAKES APPARENTLY FAILED TO ACTUATE. AGAIN ADVISED CAPT BRAKES WERE INOP. BOTH PLTS THEN APPLIED FULL PHYSICAL FORCE TO BRAKE PEDALS WITH NO APPARENT EFFECT INITIALLY. AT ABOUT 3000 FT FROM END OF RWY; FO SHOUTED 'GAR' -- CAPT HAD HANDS ON THROTTLES AT THIS POINT -- BUT CAPT ELECTED TO STOP ACFT; BELIEVING ENGS WERE IN IDLE REVERSE. ABOUT 2000 FT FROM END OF RWY; L BRAKES APPARENTLY ENGAGED AS ACFT DRIFTED SLIGHTLY L OF CTRLINE AND ACFT APPEARED TO SLOW. AT ABOUT 1500 FT ALL BRAKES ENGAGED AS ACFT RAPIDLY DECELERATED. ACFT STOPPED WITH MAIN GEAR ON RWY 04R AND THE NOSEWHEEL ABOUT 20 FT BEYOND RWY 4R END LINE ON THE HARD SURFACED OVERRUN. NOSE GEAR HAD BEEN GUIDED BTWN RWY END LIGHTS. THERE WERE NO INJURIES; THERE WAS NO ACFT DAMAGE NOR DAMAGE TO RWY OR AIRFIELD EQUIP. AFTER ACFT STOPPED FLC NOTICED EICAS ADVISORY ON LOWER CRT: 'NOSE AIR/GND DISAGREEMENT.' PAX AND FLT ATTENDANTS WERE NOTIFIED TO REMAIN IN SEATS AND ADVISED OF SITUATION. AN INSPECTION OF THE BRAKES WAS REQUESTED FROM TWR AND COMPANY IMMEDIATELY AFTER STOPPING. #2 (L) BRAKE WAS WARM; ALL OTHER BRAKES WERE COOL. REQUESTED AND RECEIVED A TOW TO THE GATE. SUPPLEMENTAL INFO FROM ACN 214244: NO DAMAGE TO ACFT OR FACILITIES OR INJURY.