During a WX briefing at 0719 ADT, the PLT was advised that VFR FLT was not recommended. Later, at 0827, he called the FSS to update his WX & filed an IFR clearance. At 0938, the ACFT departed Anchorage. During arrival at Kodiak, the ACFT was cleared for an ILS/DME-ONE APCH to RWY 25. At 1056, the PLT reported he was 8.5 DME mi north of Kodiak & level at 1600 ft. Shortly after that, radio contact was lost & the ELT sounded. Later, the ACFT was found where it collided with a mountain side at an elevation of 1450 ft. The crash site was located aprx 5 mi north of the ARPT, outside of an area where the instrument APCH would have taken the ACFT. The 1057 WX observation at the ARPT was in part: 1000 ft scattered, 3500 ft overcast, visibility 10 mi. The ARPT elev was 73 ft MSL. The WX in the mountains where the plane crashed was not verified. This was the PLT's 1st APCH to this ARPT. Radar svc was not available. The PLT's log book was not found. Reportedly, he had not flown many recent APCHs & was use to having radar assistance.