SCT CTLR EXPERIENCES 'STUCK MIKE' DURING BUSY TFC PERIOD.

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ZLA SECTOR 13 CALLED AND ADVISED THAT ACFT X WOULD BE HIGH BECAUSE OF A STUCK MIKE ON THEIR FREQ. ON INITIAL CONTACT (WHICH WAS LATE); I ISSUED A R TURN TO A HDG OF 180 DEGS AND A DSCNT TO 8000 FT. ACFT X READ BACK THE CLRNC AND THE MIKE DID NOT UNKEY. AT THAT TIME; I HAD 5 OTHER ACFT ON FREQ. I ISSUED A BASE TURN 2 TIMES TO ACFT Y. AFTER THE SECOND XMISSION; ACFT Y REPLIED THAT I WAS UNREADABLE DUE TO A STUCK MIKE. I ISSUED INSTRUCTIONS TO 2 REGIONAL ACFT; AND THEY BOTH ACKNOWLEDGED AND COMPLIED. AFTER ABOUT 2 MINS; I STARTED CHANGING ACFT TO A SPARE FREQ TO GET AWAY FROM THE STUCK MIKE. HOWEVER; ACFT Y WAS NO LONGER ON MY FREQ. (I BELIEVE ACFT Y WENT TO 121.5 AND GOT SWITCHED TO ANOTHER APCH FREQ.) APPROX 4 MINS AFTER THE STUCK MIKE STARTED; I OBSERVED ACFT Z DSNDING INTO MY AIRSPACE ON THE MOORPARK 3 ARR. I CALLED ACFT Z AT LEAST TWICE AND RECEIVED NO REPLY. ACFT Z DSNDED ON THE MOORPARK 3 ARR TO WAKER; AND THEN FOLLOWED THE TRANSITION TO THE ILS TO RWY 6L. I HAD TO VECTOR ACFT XX OFF OF THE LOC FOR RESEQUENCE TO AVOID ACFT Z. WHEN ACFT Z WAS ON ABOUT A 15 MI FINAL; MY HDOF (WHICH HAD BEEN OPEN THE WHOLE TIME) CTLR CALLED LAX TWR TO ADVISE THAT ACFT Z WAS NORDO; AND THE TWR ADVISED THAT THEY WERE TALKING TO ACFT Z. AFTER ALMOST 6 MINS; ACFT X RESOLVED THE RADIO PROB; AND 2-WAY COMS WERE RE-ESTABLISHED. I HAVE 3 OBSERVATIONS FROM THIS INCIDENT -- 1) ACFT Y ADVISED AT LEAST TWICE THAT THERE WAS A STUCK MIKE ON THE FREQ; AS IF I COULD DO SOMETHING ABOUT STOPPING IT. ALSO; SOMEONE XMITTED IN THE BLIND 'ACFT X; YOU HAVE A STUCK MIKE.' I AM SURPRISED THAT AN ACR PLT DOESN'T KNOW THAT YOU CAN'T COM WITH AN ACFT THAT HAS A STUCK MIKE. 2) THIS SIT WOULD NOT HAVE BEEN ANYWHERE NEAR AS DIFFICULT IF I HAD BEEN ABLE TO COM WITH ALL OF THE OTHER ACFT ON THE FREQ. IN THE 'OLD DAYS;' ATC HAD THE STRONGEST RADIOS; AND WE COULD OVERRIDE ACFT XMISSIONS. 3) 6 MINS IS AN ETERNITY IN AIR TFC. IT SEEMS LIKE THERE COULD BE SOME KIND OF A CUT-OUT TO PREVENT EXTENDED STUCK MIKE SITS.