LJ35 WENT OFF THE RWY WHEN THEY FOUND POOR TO NIL BRAKING ACTION ON THE RWY AFTER LNDG IN A SNOW STORM.

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FOLLOWING IS A DESCRIPTION OF EVENTS THAT OCCURRED ON THE EVENING OF JAN/WED/02 ON LNDG AT ZZZ; US. ON THE EVENING OF JAN/WED/02; I PERFORMED THE ILS APCH TO RWY 33 AT ZZZ; US. THE WX CONDITIONS AT THE FNL ARPT WERE IFR. APPROX 20 MINS PRIOR TO OUR LNDG; THE ZZZ AWOS RPTED THE CEILING TO BE 100 FT; 1 MI VISIBILITY; AND CALM WINDS. IN ADDITION; ZZZ UNICOM RPTED LIGHT SNOW. WE PERFORMED THE APCH AND BROKE OUT BTWN 300-400 FT AGL WITH THE VISIBILITY ESTIMATED AT 1 - 1 1/2 MI. THE PNF CALLED THE RWY IN SIGHT AND I SAID WE WOULD CONTINUE WITH THE LNDG. IMMEDIATELY AFTER TOUCHDOWN; I DEPLOYED SPOILERS; BRAKES; AND FULL REVERSE THRUST. BRAKING ACTION WAS POOR. UPON APPLYING SPOILERS; THE ACFT PULLED TO THE L AND I APPLIED R RUDDER; R AILERON; AND R BRAKE; WHICH SLOWED THE PULLING TO THE L. WHEN THE ACFT SPD REACHED BTWN 70-80 KTS THE ACFT BEGAN TO PULL STRONG TO THE L; WHICH I THEN APPLIED FULL R RUDDER; FULL R AILERON; AND MAX BRAKING ALONG WITH FULL REVERSE THRUST. HOWEVER; THE DRIFT INCREASED AS THE ACFT SPD SLOWED. I CONSIDERED GOING AROUND; HOWEVER; AT THIS POINT WE WERE CLOSE TO THE SIDE OF THE RWY AND UNABLE TO STOP THE DRIFT. I FELT WE COULD NOT SAFELY PWR UP AND ACCELERATE TO LIFTOFF SPD. I CONTINUED MY ATTEMPT TO STOP THE DRIFTING AND THE ACFT. JUST PRIOR TO THE 4000 FT RWY REMAINING MARKER; THE ACFT BEGAN LEAVING THE RWY STRIKING 1 RWY LIGHT AND THE 4000 FT REMAINING MARKER CONTINUING FOR APPROX 700 FT WHERE THE ACFT CAME TO A STOP. THE PNF EXITED THE COCKPIT ASKED THE PAX IF THEY WERE OK AND THEY REPLIED YES. PAX WERE THEN EVACED THROUGH THE MAIN CABIN DOOR. AS I DEPARTED THE ACFT; I OBSERVED A TOTAL ACCUMULATION BTWN 1/2 - 1 INCH OF SNOW AND SLUSH. THERE WAS A THIN LAYER OF SLUSH ON THE RWY WITH A LAYER OF SNOW ON TOP OF THE SLUSH. THERE WAS NO BRAKING ACTION RPTED FOR THIS RWY. SHORTLY AFTER THE LNDG; THE ARPT MGR OF ZZZ INSPECTED RWY 33 AND THE ARPT RWY LIGHTING SYS. AFTER HIS INSPECTION HE SAID HE WOULD LIKE TO SHOW ME THE ACFT TIRE TRACKS LEFT IN THE SNOW BEGINNING AT THE POINT OF TOUCHDOWN. HE STATED THAT HE HAD BEEN AN ACCIDENT INVESTIGATOR FOR A POLICE DEPT. AS WE LOOKED AT THE TIRE TRACKS; HE POINTED OUT A DISTINCT DIFFERENCE IN THE APPEARANCE OF THE L OUTSIDE MAIN GEAR TIRE TACK FROM THE TRACKS OF THE OTHER 3 MAIN TIRES. HE PROCEEDED TO SAY IN HIS OPINION THE TIRE APPEARED TO BE FLAT PRIOR TO LNDG. WE DROVE DOWN TO THE ACFT AND FOUND THE L MAIN TIRE WAS FLAT. IN MY OPINION; I BELIEVE THE INCIDENT WAS CAUSED BY A COMBINATION OF SEVERAL FACTORS: 1) RWY CONTAMINATION OF A COMBINATION OF SNOW AND SLUSH AND NO BRAKING ACTION RPTED; 2) THE L OUTBOARD MAIN GEAR TIRE WAS FLAT; AND 3) THE GRADE OF THE L CROWN OF THE RWY CONTRIBUTED TO THE DRIFTING EFFECT.