DURING A WX BRIEFING BEFORE TAKEOFF, THE NON-INSTRUMENT RATED PLT WAS ADVISED THAT VFR FLT WAS NOT RECOMMENDED. HOWEVER, HE DEPARTED SHEBOYGAN, WI AT APRX 1500 CST WITH NO FLT PLAN. AT DUSK, WITNESSES (NEAR THE CRASH SITE) HEARD THE ACFT MANEUVERING. ONE WITNESS HEARD THE ACFT FLY OVER HIS HOUSE, THEN CIRCLE BACK BEFORE CRASHING. ANOTHER WITNESS REPORTED THAT THE PLT SEEMED TO BE VARYING HIS ALTITUDE. HE STATED THAT THE ACFT LEFT THE AREA, THEN CAME BACK AND SUBSEQUENTLY, IT SOUNDED LIKE THE PILOT WAS TRYING TO PULL UP WHEN THE PLANE CRASHED. A THIRD WITNESS STATED THAT THE PLANE SOUNDED LIKE IT WAS IN A DIVE BEFORE IT CRASHED. THE ACFT IMPACTED IN A LEVEL FIELD AND WAS DEMOLISHED. THE MAIN WRECKAGE WAS FOUND ABOUT 7 FT FROM THE INITIAL IMPACT POINT. THE COUNTY CORONER ESTIMATED THAT THE WX WAS 200 FT OBSCURED, 1/8 MI VISIBILITY WITH RAIN AND FOG.