CE750 FLT CREW MAKES IMPROPER INITIAL CONTACT WITH N90 WITH THE CTLR READING THE TEB 5 OVER THE RADIO; CAUSING THE RPTR TO MISS THE TURN TO 280 DEGS AT 1500 FT.

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WE BRIEFED THE DEP AND HAD 1500 FT SET IN THE ALT ALERTER FOR THE TEB 5 DEP FROM RWY 24 IN TEB. THE CLRNC LIMIT FOR THIS DEP IS 2000 FT AFTER PASSING 4.5 DME FROM TEB. WHEN TEB TWR SWITCHED US OVER TO NY DEP; WE CHKED ON 'PASSING 1200 FT FOR 2000 FT;' AS THE CLRNC LIMIT STATED; HOWEVER; WE WERE GOING TO LEVEL OFF AT 1500 FT UNTIL THE 4.5 DME POINT. THE NY DEP CTLR; BELIEVING WE WERE CLBING TO 2000 FT; QUICKLY CORRECTED US BY INDICATING THAT WE SHOULD ONLY CLB TO 1500 FT UNTIL PASSING THE 4.5 DME POINT AND THEN HE BEGAN TO READ TO US THE ENTIRE TEXTUAL PROC FOR THE DEP OVER THE RADIO. DURING THIS LONG AND AGITATED SOUNDING DISSERTATION; I LEVELED OFF AT 1500 FT BUT DID NOT INITIATE THE REQUIRED TURN TO 280 DEGS AS SOON AS I REACHED 1500 FT. INSTEAD I REMEMBERED THE TURN AFTER THE CTLR FINISHED HIS DISSERTATION AT APPROX 4.0 DME FROM TEB. AT THIS POINT THE CTLR NOTICED THE DELAY IN THE TURN AND ASKED US OUR HEADING. MY FO SAID WE WERE IN THE TURN TO 280 DEGS; TO WHICH WE GOT ANOTHER COMPLETE REREAD OF THE DEP PROC; ALONG WITH A STERN REMARK ADVISING US TO SIT DOWN AND LEARN THE PROC BEFORE OUR NEXT VISIT TO TEB. I BELIEVE THIS CHAIN OF EVENTS BEGAN WITH A PHRASEOLOGY AMBIGUITY BETWEEN WHAT WE WERE CLBING TO AND WHAT WE WERE CLRED TO IN THE ATC CLRNC. THE CTLR; EXPECTING AN ERROR; PICKED THE WRONG TIME TO DISTRACT ME FROM MY DUTIES WITH HIS LONG WINDED; EDUCATIONAL SPEECH WHICH CAUSED ME TO FORGET THE TURN TO 280 DEGS. IF OUR DEP FROM THE SID PUT US IN HARM'S WAY; A CLRNC COMMAND SHOULD HAVE BEEN ISSUED TO KEEP US SAFE. NOT A LENGTHY LECTURE WHICH SHOULD HAVE BEEN HELD UNTIL WE REACHED A SAFE ALT. THIS FLT DEPARTED AFTER 7.5 HOURS OF DUTY AND LATE AT NIGHT; WHICH MAY ALSO HAVE CONTRIBUTED TO THE HEADING DEV. THE TEB 5 DEP IS A LITTLE AMBIGUOUS WHEN CHKING ON WITH DEP. IF THEY ARE EXPECTING US TO CHK IN STATING WE ARE CLBING TO 1500 FT INSTEAD OF 2000 FT; THEN A NOTE SHOULD BE ADDED TO THE SID OR THE PROC CHANGED.