320 CREW LOST COM WITH APCH CTL WHILE BEING VECTORED FOR A LOW VISIBILITY APCH AT LGA.

Narrative

AFTER HOLDING WHILE APCHING THE NEW YORK AREA; WE WERE FINALLY ON A DOGLEG TO FINAL APCH TO RWY 13 AT LGA. WE WERE AT FLAPS 2 DEGS AND 180 KTS. FUEL WAS A SERIOUS CONSIDERATION AS I FIGURED WE HAD ONLY ABOUT 5 MINS OF CONTINGENCY FUEL USING IAD AS AN ALTERNATE. JUST THEN; LGA WENT BELOW MINIMUMS; AND WE WERE VECTORED THROUGH FINAL. I GAVE THE ACFT TO THE COPLT AND ATTEMPTED TO CONTACT DISPATCH TO DISCUSS OUR ALTERNATE PLANS. WHILE WAITING FOR A RESPONSE FROM DISPATCH; I BECAME AWARE THAT WE WERE NOT HEARING TFC ON APCH CTL. SEVERAL ATTEMPTS FROM BOTH SIDES OF THE COCKPIT PRODUCED NO RESULTS. CHANGING RADIOS DID NOT HELP. I ASKED THE COPLT TO 'GET OFF THE RADIOS;' ASSUMING HE HAD A STUCK MIKE. HE SAID HE WAS 'OFF THE RADIOS.' NO CHANGE. FINALLY I SELECTED ANOTHER RADIO AND FREQ AND RE-ESTABLISHED COM. IT PROBABLY TOOK US 2-3 MINS TO RE-ESTABLISH COM. AFTER 1 MIN OR SO; WE SQUAWKED 7600M; MAINTAINING HDG; ALT; AND AIRSPD UNTIL RE-ESTABLISHING ATC COM. I ALTER DECIDED THAT THE COPLT DID NOT DESELECT HIS RADIOS; BUT MERELY WAS NOT TRYING TO XMIT. MY TERMINOLOGY; COMBINED WITH THE STRESS OF THE SIT (BAD WX; LOW FUEL; LONG DAY; LATE NIGHT; NO RADIOS IN THE NEW YORK AIRSPACE) MADE A SIMPLE PROB VERY DIFFICULT. LGA APCH VERY UNHAPPY. DIVERTED TO BWI FOR FUEL AND MAINT.