AT LAGUARDIA ARPT, WND WAS FM 320 DEG AT 16 GSTG 22 KTS. PIC RPRTD WND AT HELIPORT (ON WEST BANK OF EAST RVR) WAS FM SW.OBSTACLES WERE LOCATED ALONG WEST EDGE OF HELIPORT. PIC RPRTD HE MADE PWR CHECK, THEN BGN ROLLING TAKEOFF WITH RGT QTRG HDWND. AS ACFT WAS CLIMBING (APRX 5' AGL) OVR EAST EDGE OF HELIPORT, PIC NOTED A 'POPPING' SOUND, LOSS OF ENG PWR & MAINROTOR RPM, RISE IN EGT. ACFT BGN SETTLING & PLT TRIED DEPLOYING EMERG FLOATS, BUT DIDN'T HAVE TIME. ACFT IMPACTED WATER,ROLLED OVR & SANK. ONE PAX DID NOT EGRESS & DROWNED WITH HIS SEAT BELT STILL FASTENED. INVESTIGATION REVEALED THE ENG HAD ERROSION OF 1ST STAGE COMPRESSOR BLADES, CONTAMINATION ON BLADES/COMPRESSOR HOUSING & A LOW FUEL FLOW ADJUSTMENT OF THE FUEL CONTROL UNIT. THERE WAS EVIDENCE OF ENG SURGE/COMPRESSOR STALL. DENSITY ALT WAS 1600'. FOUR OF 5 PAX RPRTD THEYDID NOT RECEIVE INTRUCTION ON FLOATATION DEVICES/SEAT BELTS & THEY WERE NOT SHOWN THE BRIEFING CARDS. AEROSPATIALE SVC BULLETIN FOR IMPROVED TYPE 343 SEAT BELT BUCKLES (TO PREVENT BLOCKAGE OR FAILURE TO UNLOCK) WAS NOT COMPLIED WITH.