A WESTWIND 124 PLT DEVIATED FROM THE TEB SID ASSIGNED ALT WHEN DISTRACTED BY LACK OF DME INDICATIONS.

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DEPARTING TEB; NJ; RWY 24 VIA THE TEB 5 DEP; DIXIE TRANSITION; I CLBED TO 1500 FT AND THEN TURNED TO A HDG OF 280 DEGS. THE DEP CALLS FOR AN ADDITIONAL CLB TO 2000 FT AFTER CROSSING THE TEB 4.5 DME. THE TEB VOR/DME FREQUENCY WAS TUNED ON BOTH NAV RECEIVERS WITH DME SELECTED AND CHKED PRIOR TO DEP. AFTER ESTABLISHED ON THE 280 DEG HDG I NOTICED THE DME READOUT WAS FLAGGED. THE DEP CTL FREQUENCY SEEMED TOO BUSY TO ASK FOR CONFIRMATION OF MY POS SO I USED THE FLT CLOCK TO ESTIMATE PASSING 4.5 MILES FROM TEB AND THEN CLBED TO 2000 FT. UPON LEVELING ATC ASK; 'WHAT IS YOUR ALT?' WE REPLIED '2000 FT.' THE CTLR THEN TOLD US THE DEP CALLED FOR 1500 FT AT OUR CURRENT POS. IT APPEARS THAT I CLBED TOO SOON AND SHOULD HAVE USED A MORE PRECISE METHOD TO DETERMINE MY POS. DEPS FROM THIS ARPT TYPICALLY ARE VERY BUSY AND ARE A HIGH WORKLOAD FOR BOTH CREW MEMBERS. THERE IS USUALLY VERY LITTLE AIR TIME ON THE DEP FREQUENCY FOR ANYTHING OTHER THAN STANDARD COMS. THIS INFLUENCED MY DECISION TO USE A TIME ESTIMATE TO DETERMINE MY POS. IN THE FUTURE I WILL BE PREPARED TO USE ADDITIONAL MEANS SUCH AS AN NDB OR GPS TO VERIFY MY DISTANCE WHEN DEP THIS ARPT. IN EACH OF THE LAST 3 YEARS I HAVE FLOWN AIR AMBULANCE OPS OF MORE THAN 1000 HRS PER YEAR. THESE HOURS HAVE BEEN IN GA JET ACFT THROUGHOUT N; CENTRAL AND S AMERICA AS WELL AS PARTS OF EUROPE. ACCORDINGLY; I CONSIDER MYSELF TO BE AS PROFICIENT AND CURRENT AS ANYONE COULD EXPECT TO BE IN THESE HIGH DENSITY SITS. I HAVE FOUND ARRS AND DEPS AT TEB TO BE AMONG THE MOST DEMANDING THAT I HAVE EXPERIENCED. THERE ARE OFTEN NUMEROUS FREQUENCY; ALT AND HDG CHANGES ISSUED BY ATC AS WELL AS RE-RTES WHICH OFTEN OCCUR AT LOW ALTS DURING THE INITIAL CRITICAL PHASE OF FLT. I BELIEVE IT WOULD BE BENEFICIAL TO ALL IF TEB DEP PROCS COULD SOMEHOW BE SIMPLIFIED. THERE JUST SEEMS TO BE TOO MUCH GOING ON IN THE FIRST 5000 FT ON CLB.