THE RECENTLY CERTIFICATED, NON-INSTRUMENT RATED, PVT PLT FLEW INTO THE AN AREA OF LOW CEILINGS, LOW VIS, RAIN & SNW W/O FILING A FLT PLAN. NO RECORD OF A WX BRIEFING WAS FND. A SURVIVING PAX RPRTD THAT DRG FLT, THE PLT FLEW INTO CLDS THAT WERE INITIALLY SCATTERED, BUT AS THE FLT CONTD, THE CLDS BCM THICKER & DARKER. THE PAX SAID THEY FLEW INTO 'ICE CLOUDS.'ICE ACCUMULATED ON THE ACFT & THE ENG BGN TO FALTER. RPRTDLY, CARB HEAT WAS APPLIED TOO LATE TO PREVENT ENG STOPPAGE. A DISTRESS CALL WA MADE AT 1501 PST. SOON THEREAFTER, THE PLT TRANSMITTED THEY WERE 'GOING DOWN' & THEN RADAR & RADIO CTC WERE LOST. THE ACFT COLLIDED WITH TREES ON MTN TERRAIN & CRASHED. THE EMERG LOCATOR BCN (ELT) DID NOT OPER. THE ACFTWAS NOT FND UNTIL 1012 PST THE NEXT DAY APRX 1 MI FM WHERE RADAR CTCT WAS LOST. THERE WAS EVIDENCE THAT SNW & ICE HAD ACCUMULATED IN THE ENG AIR FILTER. ICE WAS FND IN THE WIRE SCREEN & PLENUM BHND THE FILTER. CARB HEAT WAS ON. RESIDENTS APRX 5 MI AWAY SAID HVY SNW WAS FALLING. TWO DEFECTIVE TRANSISTORS WERE FND IN THE ELT WHICH WOULD HAVE PREVENTED OPN.