B737-700 CAPTAIN REPORTS LOST COM SHORTLY AFTER TAKE OFF. ALL RADIOS ARE RENDERED INOPERATIVE BY AN APPARENT SHORT IN THE CAPTAIN'S COM PANEL. A SINGLE RADIO IS EVENTUALLY REGAINED AND THE FLIGHT CONTINUES TO DESTINATION.

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FLT WAS DEPARTING ZZZ AND AFTER 2 OR 3 SOLID RADIO CALLS TO DEP; I HEARD A 'CLICK' IN MY HEADSET AND WE IMMEDIATELY WENT TO 'HOT MIKE.' I WAS THEN UNABLE TO REACH DEP CTL AND IT APPEARED THE #1 VHF COM WAS INOP. TRYING #2 COM WAS UNSUCCESSFUL ALSO. AS THE FO WAS THE PF; I BEGAN TO TRY OTHER RADIOS AND HANDSETS TO REACH DEP. REALIZING THAT THIS PROB WOULD NOT BE RESOLVED QUICKLY; WE SQUAWKED 7600 AND KEPT WORKING ON THE RADIO ISSUES. MEANWHILE; WE SENT AN ACARS TO DISPATCH AND EVERYONE WAS AWARE OF OUR 'HOT MIKE/NORDO' PROB. WITHOUT COMS; WE FOLLOWED OUR LAST CLRNC TO CLB TO FL190 AND LEVELED OUT THERE. CONTINUING OUR RADIO TROUBLESHOOTING; WE DISCOVERED THAT I HAD TO UNPLUG NOT ONLY MY HEADSET; BUT THE HAND MIKE ON MY SIDE TO PREVENT THE HOT MIKE. ADDITIONALLY; WE WERE ONLY ABLE TO USE THE #1 COM WITH MY AUDIO SELECTOR XMIT SWITCH ON #2 COM AND MY FO XMITTING ON #1 COM AND USING THE SPEAKER. 'ALT/NORM' MADE NO DIFFERENCE ON THE AUDIO PANEL. SUSPECTED THAT THE CAPT'S AUDIO SELECTOR PANEL HAD AN INTERNAL SHORT. AS WE CLBED TO OUR ASSIGNED ALT OF FL410; WE WERE ABLE TO HAVE ONE RADIO THAT WORKED AND RE-ESTABLISHED COMS WITH CTR. THE REMAINDER OF THE FLT WAS UNEVENTFUL USING OUR SINGLE RADIO. AN OPERATIONAL SIDE ISSUE: IS ATC AWARE THAT IF WE ARE TOO HVY TO CLB TO OUR ASSIGNED CRUISE ALT; '10 MINS AFTER DEP' IN THE CASE OF LOST COMS; THAT WE WILL CLB TO THE HIGHEST ALT WE CAN UNTIL BURNING DOWN TO A LIGHTER WT TO CLB TO THE ATC/PDC ASSIGNED ALT? IN OUR CASE; WE WERE ABLE TO CLB UNRESTR TO OUR CLRNC ALT OF FL410; BUT I WOULD HAVE CLBED TO FL390 UNTIL LIGHT ENOUGH TO REACH OUR CLRNC ALT. AN ELECTRICAL MALFUNCTION INTERNALLY IN THE AUDIO PANEL OR #1 VHF COM. BETTER QUALITY CTL DURING MANUFACTURER.