THE PLT WAS CLEARED FOR AN ILS RWY 35 APPROACH & GIVEN THE KANSAS CITY DOWNTOWN ARPT (23 MI NE) WX AS 900 FT BROKEN & 6 MI VISIBILITY. THE TOWER WAS CLOSED & THE CONTROL ZONE WAS NOT IN EFFECT RAISING MINIMUMS. THE PLT STATED HIS ILS GLIDE SLOPE INDICATION WAS ERRATIC AT THE OUTER MARKER SO HE ELECTED TO CONTINUE A STRAIGHT-IN LOCALIZER ONLY APPROACH. HE SAID HE DESCENDED TO MDA OF 1400 FT (335 FT AGL) BUT THE ACFT WAS STILL IN CLOUDS. HE SAID AS HE WAS CHECKING VHF CONTROL HEAD TO INSURE PROPER FREQ SETTING FOR ACTIVATING THE APPROACH LIGHTS, THE ACFT STRUCK THE GROUND. INITIAL IMPACT WAS 1 MI SOUTH OF THE APCH END OF RWY 35 & ABOUT 100 YDS LEFT OF THE INBOUND ILS LOCALIZER COURSE. THE MDA IS INCREASED 100 FT WHEN THE CONTROL ZONE IS NOT IN EFFECT. NO MALFUNCTIONS OF THE ACFT'S ILS RECEIVERS OR #1 OBS WAS FOUND. A FLT INSPECTION OF THE ILS WAS SATISFACTORY. IN ADDITION TO 7 HOURS OF DUTY TIME ASSOCIATED WITH THE FLT, THE PLT HAD WORKED A NORMAL DUTY DAY ON 5/11 INVOLVING MANAGEMENT FUNCTIONS & HAD RESTED 3-4 HRS PRIOR TO THE FLT.