About 10 min after takeoff at 1005 MDT, the plt was cleared to climb to FL 190. This was ATC's last communication with the acft. At 1030:39, the controller attempted to contact the plt to advise that he had lost radar contact & to recycle the transponder & squawk 6062. There was no response. Two witnesses reported seeing the acft just before it impacted the ground. According to them, they saw fire &/or an explosion before impact & one witness reported the acft broke up after it came below an estimated 1000 to 1200 ft ceiling. However, the wreckage was scattered over a 2 mi area. An exam revealed evidence of a catastrophic in-flt breakup from overload which included positive overload of both wings. Radar data showed that just before radar contact was lost, the acft's speed varied between 221 & 272 kts, heading varied from 072 to 014 deg & vertical velocity varied from +300 to -2400 ft/min. Thunderstorms, turbc, rain & cld tops to 25,000' were reported. Probable lgt to mod icing in clds above the freezing lvl (14,000'). Acft had wx radar aboard.