AN AC690 PLT DISTR BY A MASTER CAUTION LIGHT AFTER TKOF EXCEEDED THE TEB 5 DEP'S 1500 FT RESTR.

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THIS WAS MY SECOND TRIP IN THE AC690B SINGLE PLT AT NIGHT. IT WAS MY THIRD LEG OF THE DAY. WE WERE ON OUR WAY HOME AFTER DELIVERING A PATIENT TO THE TEB ARPT IN NJ. I WAS CLRED VIA THE TEB 5 DEP AND WAS VERY FAMILIAR WITH THE 'HOT SPOTS' ON THAT SID; SINCE I WAS VERY NEW TO THE AIRPLANE AND TO TEB. I DEPARTED FROM RWY 24 AND WAS PLANNING TO CLB TO 1500 FT; MAKE THE TURN THEN CLB TO 2000 FT. AT APPROX 1300 FT; JUST BEFORE I WAS GOING TO LEVEL OFF; A RED WARNING LIGHT ILLUMINATED ON MY ANNUNCIATOR PANEL AND DISTRACTED ME FROM LEVELING AT 1500 FT. IT WAS A 'DOOR' WARNING AND SINCE I WAS BRAND NEW TO THE AIRPLANE; I WAS ALARMED ENOUGH TO GLANCE BACK AT THE DOOR TO LOOK FOR ANYTHING UNUSUAL AND BY THE TIME I LOOKED BACK AT MY INSTRUMENTS; I WAS PASSING THROUGH 1800 FT. I IMMEDIATELY STARTED A DSCNT BACK TO 1500 FT; BUT THE CTLR NOTICED THE ALT DEV AND SAID SINCE I HAD ALREADY PASSED THE REQUIRED ALT; JUST KEEP CLBING TO 8000 FT. I THEN CLBED AS DIRECTED AND THE REMAINDER OF THE FLT WAS UNEVENTFUL. THIS IS A PERFECT EXAMPLE OF HUMAN PERFORMANCE. I HAVE OVER 20 YRS AS AN AIRLINE PLT WITHOUT A SINGLE ALT DEV; BUT AT A NEW ARPT IN AN UNFAMILIAR AIRPLANE WITH A POTENTIAL EMER WARNING; I LOST MY SITUATIONAL AWARENESS ENOUGH TO DEVIATE FROM THE SID. I HAD THE ENTIRE SID COMMITTED TO MEMORY; BUT I STILL BECAME DISTR. DURING THE TKOF PHASE; A MASTER WARNING IS IMPOSSIBLE TO IGNORE AND A COMPLICATED DEP; SUCH AS THE TEB 5 ADDS TO THE WORKLOAD. I DID NOT TELL THE CTLR ABOUT THE WARNING; AS HE WAS QUITE BUSY AND CLRED ME TO 8000 FT SINCE THERE WAS NO CONFLICT WITH OTHER TFC.