MD90 EXPERIENCES RADIO FAILURE DURING DSCNT OUT OF ZLC AIRSPACE INTO S56 AND SLC TWR.

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WE WERE CLRED DIRECT TO LHO EXPECTING LHO 2 ARR TO SLC. WE WERE GIVEN A CTR FREQ CHANGE AND GOT NO RESPONSE. WE RETURNED TO PREVIOUS FREQ AND WERE UNABLE TO CONTACT THERE EITHER. WE TRIED THE OTHER RADIO AND OTHER MIKES AND ALTERNATE AMPS; BUT STILL NO CONTACT. JUST PRIOR TO LHO; WE DID GET A MOMENTARY XMISSION FROM ZLC TO TURN L TO 190 DEGS AND DSND TO 15000 FT. WE RESPONDED; GOT NO FURTHER RESPONSE AND COMPLIED. AT THIS POINT; WE INTERCEPTED ARR S OF LHO TO CARTR FIX; AND SQUAWKED 7600. WE CONTINUED TO ATTEMPT COM ON ALL RADIOS AND 121.5 AS WELL. AS WE NEARED SLC; I DIRECTED FO TO TURN R DIRECT TO OGD VOR AND BRIEFED HIM THAT WE WOULD ENTER HOLDING AT OGD AND DSND TO 10000 FT IN HOLDING AND THEN FOLLOW PUBLISHED ROUTINGS TO ILS RWY 16L AT SLC. WHILE NBOUND TO OGD; WE AGAIN RECEIVED A MOMENTARY XMISSION FROM ZLC TO TURN R TO 150 DEG HDG AND CONTACT SLC APCH. WE AGAIN COMPLIED AND WERE UNABLE TO GET ANOTHER RESPONSE. (FYI; WE HEARD NO OTHER RADIO CALLS FROM ATC OR ACFT DURING THIS ENTIRE SIT.) WE AGAIN DECIDED TO GO BACK TO OUR ORIGINAL PLAN AND TURNED R BACK TO OGD. AGAIN; WHILE NBOUND; WE BEGAN RECEIVING SLC APCH; BUT COULD NOT XMIT. WE ACKNOWLEDGED VECTORS; ALTS AND CLRNCS BY IDENT AND RECEIVED A GREEN LIGHT FROM TWR AS CLRNC TO LAND ON RWY 16R. A FOLLOW-ME WAS STANDING BY TO LEAD US TO THE GATE. IT APPEARED (POSTFLT) THAT THE PROB WAS A STUCK MIKE RELAY IN MY COM PANEL BOX. WHAT WAS DECEIVING TO OUR INFLT PROB ANALYSIS; IS THAT WE BOTH GOT NORMAL SIDE TONES WHEN WE ATTEMPTED XMISSIONS. HAD WE KNOWN; WE WOULD HAVE PROBABLY CONFIGURED OUR COM TO LISTEN/XMIT ONLY ON FO'S PANEL AND SET UP MY SIDE TO A NON ESSENTIAL POS. THE HIGH TERRAIN AND KNOWN HIGH DENSITY TFC WERE CONCERNS THAT OCCUPIED OUR FOCUS ALLOWING LESS TIME FOR TROUBLESHOOTING. SUPPLEMENTAL INFO FROM ACN 500012: LEVEL AT 15000 FT; 250 KTS; 190 DEG HDG; AND JUST N OF THE SLC VORTAC; SQUAWKING 7600; WE RECEIVED A TA. WE WERE IMC; AND MONITORED TCASII. OTHER ACFT CAME WITHIN 1600 FT; AROUND 1 MI; NO CLOSER. BELIEVE OTHER ACFT TO BE ANOTHER ACR. SOON AFTER WE WERE ABLE TO MONITOR SLC APCH; AND RESPOND WITH IDENTS. MADE UNEVENTFUL ILS RWY 16R APCH AND LNDG. CALLBACK CONVERSATION WITH RPTR ACN 500267 REVEALED THE FOLLOWING INFO: RPTR WAS VERY HAPPY THAT THINGS DID NOT GET ANY WORSE; ANALYST CONGRATULATED THE FLC FOR CORRECT ACTIONS AND GOOD TRAINING.