B737-300 PF SETS AND FLIES WRONG SID DEP HDG AT LGA.

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LGA WAS DEPARTING ON RWY 13 WITH A WHITESTONE CLB. CLRNC WAS RECEIVED VIA PDC WITH AN ASSIGNED FREQ 120.4. THE LGA 8 DEP WITH THE WHITESTONE CLB WAS BRIEFED DURING THE BEFORE START CHKLIST AND AGAIN IN MORE DETAIL DURING THE BEFORE TKOF CHKLIST. AFTER TKOF AND CLBING ON 175 DEG HDG UNTIL 2.5 DME; I INSTRUCTED THE FO TO SELECT 040 DEG HDG ON THE MCP; WHICH HE DID. HE APPARENTLY LOOKED AT HIS DEP PLATE TO CONFIRM THE HDG AND SAW 340 DEG HDG LISTED FOR THE MASPETH CLB AND SET THAT HDG. DURING THE CLBOUT AND HDG CHANGE; WE WERE TRYING TO CONTACT DEP ON 120.4; ALONG WITH ANOTHER ACFT. I TOLD THE FO TO GO BACK TO TWR AND GET A GOOD DEP FREQ. TWR TOLD US THAT DEP WAS NOW ON 120.8. WHILE TURNING THROUGH 040 DEGS; I QUESTIONED THE FO ON THE HDG AND HE SAID IT WAS 340 DEGS. (I WAS THINKING THAT TWR MIGHT HAVE CHANGED OUR HDG AND I DID NOT HEAR.) WHEN WE ATTAINED THE NEW FREQ AND CHKED IN; THE CTLR ASKED US WHAT HDG WE WERE ON. THE FO TOLD HIM AND THE CTLR SAID THAT WE MIGHT WANT TO CHK THE DEP ASSIGNED HDG. THERE WERE NO CONFLICTS WITH OTHER TFC ON THE TCASII AND NO ACFT WITHIN 5 MI. ALTHOUGH THE DEP WAS THOROUGHLY BRIEFED; A MISUNDERSTANDING WAS PRESENT -- COMBINED WITH ATC CHANGING THE DEP FREQ. (USUALLY LGA DOES AN EXCELLENT JOB KEEPING ACFT INFORMED WHEN CHANGES ARE MADE IN FREQ; HDG OR DEP.)