A B737-800 FLC WITH AN MEL'ED TCASII HAS TO PERFORM AN EVASIVE ACTION TURN WHILE HAVING PROBS WITH THEIR AUTOPLT AND COM RADIOS WITH N90; NY.

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DEPARTING LGA ON AN INITIAL CLBOUT FROM RWY 4; OUR CLRNC WAS TO TURN TO A 360 DEG HDG AND 5000 FT. AN ADDITIONAL VECTOR WAS GIVEN TO 270 DEG HDG TO INTERCEPT ON COURSE TO LANNA INTXN. DUE TO THE AUTOPLT NOT ENGAGING PROPERLY; I CONTINUED TO HAND FLY TO 5000 FT WHERE IT WAS ENGAGED. DURING THE CLB WE RECEIVED A FREQ CHANGE TO NEW YORK TRACON. THE CAPT CALLED 3 TIMES ON THE NEW FREQ WITHOUT A RESPONSE RECEIVED FROM NEW YORK. AFTER CHKING THE RADIO/EQUIP; HE RETURNED TO THE DEP FREQ. NOW; ON THE OLD FREQ; THERE WAS ALSO NO RESPONSE. CAPT WENT BACK TO NEW YORK TRACON. AT THAT TIME; I NOTICED ANOTHER ACFT CLBING IN CLOSE PROX TO MY ACFT. I MADE A TURN AWAY AND SIMULTANEOUSLY THE CAPT WAS ABLE TO REACH NEW YORK TRACON. CAPT NOTIFIED NEW YORK OF OUR SIT AND WE WERE VECTORED AWAY FROM TFC. CONTRIBUTING FACTOR FROM PLT/CTLR PERSPECTIVE WAS AN INABILITY OF TIMELY RADIO COMS/COORD IN A HIGH DENSITY AVIATION ENVIRONMENT. IN ADDITION; ON THIS ACFT; WE WERE DISPATCHED WITHOUT AN OPERATIONAL TCASII SYS WHICH SHOULD HAVE GIVEN AN EARLY TFC CONFLICT NOTIFICATION. THE COM BREAKDOWN WAS VERY SHORT YET LED QUICKLY TO UNSAFE FLYING IN THE NEW YORK AREA.