ACFT EQUIP PROB. LOST COM WITH CTR DUE TO RADIO PROB. STARTED DSCNT LATE DUE TO THE LOST COM AND MISSED XING ALT RESTR. FLC SQUAWKED 7600 AND MADE RAPID DSCNT. RADIO PROB WAS CORRECTED AND REMAINDER OF FLT WAS NORMAL.

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WE STARTED A SLOW DSCNT FROM FL350 TO FL290 APPROX 140 MI FROM DFW. APCHING FL290; I ASKED FOR A LOWER ALT BUT GOT NO REPLY FROM ZFW. MORE ATTEMPTS WERE MADE ON BOTH THE L; R AND CTR VHF RADIOS ON VARIOUS FREQS. INITIALLY; WE BELIEVED THAT ZFW HAD RADIO PROBS SINCE WE COULD STILL HEAR OTHER XMISSIONS; BUT THEN WE LOST EVERYTHING AND KNEW THAT WE HAD THE PROB. ALL HEADSETS WERE DISCONNECTED; SWITCH POS CHKED; AND MIKES APPEARED TO NOT BE STUCK. WE SQUAWKED 7600 AND BEGAN A RAPID DSCNT; ATTEMPTING TO MEET THE EXPECTED XING ALT OF 9000 FT AT BRAID ON THE BLUE RIDGE 7 ARR. WE MISSED THIS ALT BY 2000-3000 FT. THE HAND-HELD MIKE; WHICH IS NOT NORMALLY USED FOR FLT; WAS DISCONNECTED FROM THE FO POS AND GIVEN TO THE OBSERVER FOR HIM TO ATTEMPT CONTACT ON ANY APCH FREQ. APPARENTLY THE HAND-HELD MIKE WAS SHORTING OUT ALL POS SINCE WE WERE ABLE TO CONTACT APCH CTL AS WE APCHED 9000 FT. AN UNEVENTFUL APCH AND LNDG WERE MADE. AFTER LNDG; A THOROUGH DEBRIEF WAS CONDUCTED WITH MAINT. ALL HEADSETS AND THE HAND-HELD MIKE WERE REPLACED AND RADIOS WORKED WELL ON THE RETURN FLT. IT WAS DIFFICULT FOR EVERYONE IN THE COCKPIT TO BELIEVE THAT WE COULD HAVE LOST OUR ABILITY TO XMIT AND RECEIVE FROM 3 RADIOS AT 3 DIFFERENT STATIONS IN A NEW B767 ACFT. WE DIDN'T WANT TO COME INTO DFW ARPT WITH NO COMS. BY ATTEMPTING TO CURE THE PROB AND REGAIN OUR COMS WITH ZFW; WE DELAYED OUR DSCNT WHICH NECESSITATED A HIGH RATE DSCNT AND THEREFORE WE WERE ABOVE THE EXPECTED XING ALT OF 9000 FT AT BRAID. IF THE LOSS OF RADIOS HAD OCCURRED EARLIER IN THE FLT; WE WOULD HAVE BEGUN OUR DSCNT AND STAYED ON A PATH THAT WOULD HAVE ALLOWED US TO CROSS BRAID AT THE EXPECTED ALT AND SPD.