A B737-300 SLIDES OFF THE END OF RWY 4R DURING A ROLLOUT TO THE END AT ORD; IL.

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ORD TWR ISSUED US A LNDG CLRNC TO RWY 4R WITH A REMARK TO 'ROLL TO THE END.' WE LANDED ON SPD IN THE TOUCHDOWN ZONE FOLLOWING A STABILIZED APCH. THE RWY WAS WET AND THE WIND WAS CALM. AS PF; I INITIATED REVERSE THRUST SHORTLY AFTER TOUCHDOWN. THE SPOILERS DEPLOYED AND WE BEGAN TO DECELERATE. I BEGAN TO APPLY BRAKES IN ANTICIPATION OF OUR EXIT ONTO TXWY D AT THE END OF RWY 4R. THE CAPT CALLED OUT '80 KTS.' I STOWED THE REVERSERS AND A POSITIVE XFER OF CTL WAS MADE TO THE CAPT. I THEN CALLED OUT '60 KTS.' AT SOME POINT AFTER THE 60-KT CALL; THE BRAKES BECAME INEFFECTIVE. I GOT UP ON THE BRAKES WITH THE CAPT AND APPLIED FULL BRAKE PRESSURE TO NO EFFECT. THE NOSEWHEEL AND L MAIN DEPARTED THE PREPARED SURFACE; WITH THE L MAIN COMING TO REST IN THE GRASS AND THE NOSEWHEEL IN THE OVERRUN OF RWY 4R. WE STARTED THE APU; SHUT DOWN BOTH ENGS AND SECURED THE ACFT WITH THE PARKING CHKLIST. WE KEPT THE PAX ON BOARD UNTIL AIRSTAIRS WERE BROUGHT FOR THEM TO DEPLANE. THERE WERE NO INJURIES. I BELIEVE WE GOT INTO A SIT OF VISCOUS HYDROPLANING ON THE LAST 1/3 OF THE RWY. BRAKING WAS GOOD ON THE FIRST 2/3 OF RWY 4R; AND ESSENTIALLY NIL ON THE LAST 1/3. A TSTM HAD RECENTLY PASSED OVER THE ARPT. THE WATER ON THE RWY COUPLED WITH RUBBER DEPOSITS AND THE PAINTED THRESHOLD LED TO DECREASED BRAKING EFFECTIVENESS. I SUGGEST THAT WHEN RWY 4R IS WET; ORD TWR INSTRUCT ACFT TO TURN AT TXWY Q INSTEAD OF THE END. THAT WAY; THE ACFT MAY BRAKE IN AN AREA WHERE THERE IS NOT AS MUCH RUBBER DEPOSITS OR PAINT. THERE WOULD ALSO BE RWY REMAINING IF THE ACFT BEGAN TO SLIDE JUST BEFORE THE PLANNED EXIT.