B737 LNDG LAX 25L. STUCK MIKE ON FREQ BLOCKED COM. OBSERVED RWY DEP TFC NOT MOVING; AND INITIATED GAR TURNING SOUTH NOT TO OVERFLY TFC.

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ON A VISUAL APCH TO RWY 25L AT LAX AND USING THE ILS RWY 25L APCH AS A BACK-UP APCH IN VMC; WE WERE CONFIGURED TO LAND INSIDE THE OM. LAX TWR HAD GIVEN US A LNDG CLRNC AND ADVISED US OF A B757 ON LNDG ROLLOUT AND THAT A BRASILIA ACFT WOULD BE TAKING THE RWY FOR DEP; PRIOR TO OUR ARR. AS WE APCHED SHORT FINAL; BOTH ACFT WERE ACQUIRED VISUALLY. AFTER THE BRASILIA TAXIED INTO POS ON RWY 25L AHEAD OF US; THE TWR RADIO FREQ BECAME INTERFERED WITH BY WHAT SOUNDED LIKE A STUCK MIKE ON THE FREQ (120.95). THE XMISSIONS ON THE FREQ THAT FOLLOWED WERE GARBLED AND UNREADABLE. IT SOUNDED AS THOUGH THE TWR WAS ATTEMPTING TO CLR THE BRASILIA ON THE RWY AHEAD OF US FOR TKOF. THE BRASILIA WAS NOT RESPONDING AND REMAINED ON THE RWY IN POS; CONTINUING TO BLOCK THE TOUCHDOWN ZONE. AT APPROX 700 FT AGL WE EXECUTED A GAR CLBING STRAIGHT AHEAD. AS THE GAR MANEUVER WAS ACCOMPLISHED; THE BRASILIA ACFT ON THE RWY COMMENCED A TKOF ROLL. WE OFFSET SLIGHTLY TO THE S TO AVOID FLYING OVER THE BRASILIA'S TKOF LEG. AT THIS TIME WE HEARD OUR FIRST XMISSION OVER GUARD FREQ (121.5) ASSIGNING US A GAR HDG AND DEP FREQ. WE CONTACTED LOS ANGELES DEP CTL AND COMPLIED WITH THE ASSIGNED CLBOUT PROC. LOS ANGELES DEP CTL PROVIDED US WITH RADAR VECTORS FOR A RETURN APCH AND LNDG ON RWY 25L. AS FAR AS WE KNOW; NO SEPARATION CRITERIA WAS VIOLATED. SUPPLEMENTAL INFO FROM ACN 748016: AFTER WE LANDED; TWR ADVISED US THAT THE ACFT IN POS HAD A STUCK MIKE. IT WAS VERY DIFFICULT TO SEE THE BRASILIA IN POS AT NIGHT. HAD THE CTLR NOT TOLD US ABOUT THE ACFT 'IN POS' WHEN WE RECEIVED OUR LNDG CLRNC; I AM NOT SURE I WOULD HAVE SEEN THE PLANE AND TAKEN OUR GAR.