THE NON-INSTRUMENT RATED PILOT ENCOUNTERED INSTRUMENT METEOROLOGICAL CONDITIONS (LOW CEILINGS AND REDUCED VISIBILITIES IN FOG) WHILE RETURNING TO THE HOME BASE AIRPORT. A WITNESS SAW THE AIRPLANE DESCEND NOSE FIRST INTO A FIELD LOCATED ABOUT 3 MILES FROM THE DESTINATION AIRPORT. HE DESCRIBED SEEING THE TOP OF THE WINGS AND FUSELAGE BRIEFLY BEFORE IMPACT, AND STATED THE AIRPLANE APPEARED TO BE ALMOST PERPENDICULAR TO THE GROUND. POST-ACCIDENT INVESTIGATION REVEALED NO EVIDENCE OF PRE-IMPACT MECHANICAL MALFUNCTION. WEATHER AT DUPAGE COUNTY AIRPORT, 15 MILES SOUTHEAST OF THE ACCIDENT SITE, WAS REPORTED TO BE: SKY PARTIALLY OBSCURED, 300 OVERCAST, 1 MILE VISIBILITY, FOG, TEMPERATURE 39 DEGREES FAHRENHEIT (F), DEW POINT 39 DEGREES F, WINDS OUT OF 060 DEGREES AT 12 KNOTS. LOCAL RESIDENTS REPORTED HEARING THE ENGINE NOISE OF A LOW FLYING AIRPLANE, AND RELATED THAT THE WEATHER HAD DETERIORATED RAPIDLY THAT AFTERNOON.