ABOUT 16 MIN AFTER TAKEOFF, WHILE CRUISING AT 6000' MSL IN IMC, THE PLT TRANSMITTED 'SIKORSKY 507' (CALL SIGN OF ACFT HEFREQUENTLY FLEW). THE ATC CTLR WAS TALKING TO ANOTHER FLT & DID NOT RESPOND. ABOUT 1 MIN LATER, RDO & RADAR CONTACT WERELOST & THE HELICOPTER CRASHED WHILE IN A STEEP/HI SPD DSCNT. AN INV SHOWED THAT DRG IMPACT, IT WAS IN A 10 DEG NOSE UP, 12 DEG RGT BANK ATTITUDE. WITNESSES, WHO HEARD THE HELICOPTER, RPRTD THE ENGS WERE RUNNING AT HI PWR BFR IMPACT. THEY DESCRIBED THE WX AS LOW OVERCAST WITH RAIN, FOG & POOR VIS. RADAR DATA SHOWED THAT JUST BFR ENTERING A DSCNT, THE HELI- COPTER WAS ON A SW HDG AT 138 KTS, WHEN ITS HDG & SPD BGN TO VARY. IT SLOWED TO 116 KTS, TURNED LEFT TO 229 DEG, THEN ENTERED A RGT DSCNDG SPIRAL & CRASHED. NO PREIMPACT PART FAILURE/MALFUNCTION WAS FND. PREV DISCREPANCIES NOTED OF N5AZ'SELEC FLT INSTRUMENT SYS (EFIS) ON 5/5/86 & 5/27/86; CAUSE OF 1ST WAS NOT FND; 2ND WAS RELATED TO A POPPED CKT BRKR. NO KNOWN EFIS PRBLM ON ACDNT FLT, BUT ACFT WAS BADLY DMGD. PLT HAD 1525 HRS IN S-76A, ONLY 30 HRS IN S-76B (WITH EFIS).