Before takeoff, the non-instrument rated pilot was briefed by the weather service office for a VFR, no-flight-plan flight. In flight, the pilot received a briefing from an AFSS and was told that VFR flight was not recommended. The pilot informed center that he was climbing to 7,000 feet to stay on top. When he was approaching his destination, he informed approach control that he was on top of an overcast and was trying to find a place to get down. After radio and radar contact was lost with this airplane, another approach controller observed a slow moving primary radar target south of the destination airport, but after it was lost, he was unable to determine its last known location, or its identity. The airplane was in near level attitude at tree impact, then near 60 degree down path to terrain. Damage to trees, and propeller indicate engine power being developed at impact. Weather in area not known. Weather study shows forecast of heavy rain, reduced visibilities, moderate turbulence below clouds.