The non-instrument rated pilot first filed an IFR flight plan before obtaining a weather briefing. Light to moderate rime icing was forecast from 5,000 to 16,000 ft. At 1541 the ARTCC controller noticed the Mode C altitude report was 1,300 ft lower than the assigned altitude of 10,000 ft, and descending. The pilot responded to the controller's inquiry that 'I cannot maintain altitude'. At 1543 radio and radar contact was lost. An airline flight reported picking up moderate rime ice while flying in the area of the accident site. A ground witness reported that at the time of the accident a thunderstorm was overhead, accompanied by lightning, thunder, hail, and moderate snow and rain showers. The witness also heard a loud 'winding up engine sound followed by a large bang'. The last pitot static system test and calibration was recorded on 7/8/86. The pilot had received about 44 hrs dual instrument training during the first 6 months of 1986.