B737-500 FLC FAILED TO HEAR AN ATC CLRNC OR CONSEQUENTLY; COMPLY. CTLR INTERVENED.

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DURING DSCNT INTO SLC; I LEFT THE ATC FREQ TO PICK UP ATIS ON SECOND RADIO. DURING THIS TIME APCH CTL ISSUED INSTRUCTIONS TO 'MAINTAIN PRESENT HDG' (280 DEGS). THE OTHER PLT DID NOT HEAR THE INSTRUCTION AND DID NOT READ IT BACK. WHEN I RETURNED TO ATC FREQ WE TURNED N TOWARD SLC AS WE CROSSED FFU VOR. APCH CTL ASKED US WHAT OUR HDG WAS AND I RESPONDED. HE TOLD US OUR LAST INSTRUCTION WAS TO MAINTAIN PRESENT HDG; NOT TO TURN. I ACKNOWLEDGED THIS AND A NEW HDG WAS ASSIGNED. ON THE GND WE CALLED APCH TO DISCUSS THE EVENT. HE STATED HE WAS BUSY AND DIDN'T NOTICE THAT HIS INSTRUCTIONS HAD NOT BEEN READ BACK. ATIS WAS DIFFICULT TO HEAR; WE WERE CLOSE TO SLC AND NEEDED THE INFO TO PLAN OUR APCH IN A TIMELY MANNER -- THAT'S WHY I TURNED THE ATC RADIO DOWN AND CONCENTRATED ENTIRELY ON COLLECTING THE ATIS INFO. THIS SIT REMOVED ME FROM THE LOOP; LEAVING NO REDUNDANCY IN THE COCKPIT. THE OTHER PLT WAS AWARE THAT I WAS OFF FREQ YET IN THE CONFUSION OF FLYING; OPERATING RADAR (TSTM AVOIDANCE) AND HVY RADIO TFC; THE ASSIGNED HDG CALL WAS MISSED. APCH WAS VERY BUSY AND MISSED OUR LACK OF READBACK. ASIDE FROM ALL PARTIES LISTENING CLOSER; I THINK THE ONLY REAL WAY TO AVOID ALL SIMILAR OCCURRENCES IN THE FUTURE IS TO HAVE ATIS INFO PUT IN ELECTRONIC FORMAT AND AVAILABLE THROUGH ACARS. SUPPLEMENTAL INFO FROM ACN 314190: AFTER FFU VOR WE MADE A 90 DEG RIGHT TURN AS PER THE FLT PLAN ROUTING. WE WERE QUERIED AS TO OUR HDG. THAT IS WHEN WE FOUND OUT THEY WANTED US TO BE ON A W HDG. WE THEN ASKED WHAT HDG DO THEY NOW WANT US ON; AND WE COMPLIED. I COULD HAVE LISTENED UP A LITTLE BETTER FOR THE RADIO CALL THAT THEY SAID I MISSED; BUT I FEEL THAT THE CTLR SHOULD HAVE LISTENED FOR MY REPLY THAT I DID NOT MAKE.