B737-300 FLT CREW HAS LOST COM DURING ARR INTO RIC.

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WHILE IN CRUISE FLT; RADIO COM WAS LOST WITH ZDC SHORTLY AFTER CLRNC WAS GIVEN TO DSND AT PLT'S DISCRETION TO CROSS RIC VOR AT FL240. I NOTICED THAT IT WAS VERY QUIET ON THE RADIO AND PUSHED THE SQUELCH BUTTON ON COM #1 AND HEARD NOTHING. I TRIED COM #2 AND THAT DIDN'T WORK EITHER. WE CHKED ALL COMBINATIONS OF 'TX' AND 'RX' ON BOTH CAPT'S AND FO'S AUDIO SELECT PANEL; AND NEITHER OF US COULD 'TX' AT ALL. I FINALLY WAS ABLE TO 'TX' ON COM #2 AND 'RX' ON COM #1 ON 2 DIFFERENT FREQS. ZDC HANDED US OFF TO THE NEXT SECTOR AND COULDN'T 'TX OR RX' ON THAT FREQ EITHER. WENT BACK TO THE PREVIOUS FREQ AND COULDN'T SPEAK WITH ANYONE. I UNPLUGGED BOTH MY HEADSET AND HAND MIKE TO SEE IF THAT WAS CAUSING A SUSPECT STUCK MIKE ON OUR ACFT. THAT DIDN'T WORK EITHER. I SELECTED 7600 ON THE XPONDER AND BEGAN BLIND 'TX' ON 121.50 TO TRY TO RAISE ANYONE. FINALLY WAS ABLE TO 'TX' ON 121.50 AND INSTRUCTIONS WERE RELAYED THROUGH THAT RADIO. UNSURE WHETHER CTR/APCH/TWR COULD HEAR ME. I WOULD HIT THE IDENT TO ACKNOWLEDGE EVERY TIME INSTRUCTIONS WERE GIVEN. LANDED WITHOUT ANY FURTHER PROBS AND HAD MAINT MEET THE ACFT TO TROUBLESHOOT RADIO PROBS.