THE FLT DEPARTED BATON ROUGE (BTR) FOR THE PLTS STATED DEST OF ALEXANDRIA, WHICH WAS 78 MILES ON A BEARING OF 301 DEG, AT 0836 CDT. AFTER DEP THE BTR LOCAL AREA THERE WAS NO RADIO CONTACT WITH ANY ATC FACILITY. THE TRANSPONDER CONTINUED TO TRANSMIT A CODE 1200 UNTIL RADAR CONTACT WAS LOST AT 1145:32 CDT. IMPACT OCCURRED DURING A POWER-OFF UNCONTROLLED DESCENT APRX 3 HRS AND 24 MIN AFTER TAKEOFF ABOUT 310 DEG AND 520 NAUTICAL MILES FROM BTR. THERE WERE NO DEVIATIONS FROM THAT COURSE. ONLY A TRACE OF UNUSABLE FUEL WAS FOUND IN THE WRECKAGE WITH NONE DISCOVERED IN FUEL LINES. LINE OF SIGHT DISTANCE CALCULATIONS FROM ATC SITES REVEALED THAT THE ACFT ACHIEVED AN ALTITUDE OF AT LEAST 12,800 FT. ACFT SPEED CHANGES FROM RECORDED RADAR DATA AND PERFORMANCE INFO FROM THE MANUFACTURER INDICATED THAT THE ACFT CLIMBED TO AN ALT OF APRX 18,685 FT MSL. THE CABIN PRESSURIZATION SWITCH WAS FOUND IN THE OFF POSITION AND ONBOARD OXYGEN WAS NOT UTILIZED.