BFR TKOF, THE PLT OBTAINED A WX BRIEFING & FILED AN IFR FLT PLAN. HE TKOF AT APRX 0816 CDT. AT APRX 0820, THE ACFT WAS RADAR IDENTIFIED ABOUT 1 MI SOUTH OF ROUND ROCK, TX, HEADING EASTBOUND. THE PLT WAS ISSUED AN IFR CLNC, AS FILED, & WAS CLRED TO CLIMB FROM 2000 TO 7000 FT. APRX 1 MIN LATER, AN ATC CONTROLLER NOTICED THAT THE ACFT HAD TURNED NORTHBOUND & QUERIED THE PLT, BUT THE PLT'S RESPONSE WAS UNREADABLE. SHORTLY AFTER THAT, RADAR & RADIO CONTACT WERE LOST. A WITNESS STATED THAT SHE HEARD "THE ROAR OF AIRPLANE ENGINES", BUT ALSO STATED "IT SEEMED TO BE HAVING ENGINE TROUBLE." SHE REPORTED THAT THE ACFT BANKED RGT AS IF TO LAND, BUT HIT A FENCE, THEN A NUGE FIRE ERUPTED. THE ACFT WAS DEMOLISHED BY FIRE. BOTH ENGS WERE DISASSEMBLED & INSPECTED, BUT NO FAILURES WERE NOTED, EXCEPT WHERE THE LEFT ENG OIL SUMP WAS PUSHED IN. AT AUSTIN, TX, THE WX (IN PART) WAS: 400 FT OVC, VIS 1/2 MI WITH FOG.