AIRPLANE CRASHED DURING A UNCONTROLLED DESCENT, FOLLOWING A TURBULENCE UPSET AT FL370. THE UPSET OCCURRED AS A RESULT OF CLR AIR TURB ASSOCIATED WITH A VIP LVL 6 THUNDERSTORM LOCATED WITHIN 7 MILES OF THE LAST POS OF THE AIRPLANE. AFTER THE UPSET, THE AIRPLANE PENETRATED AND DESCENDED THRU THE CELL WHICH CONTAINED LIGHTNING, EXTREME TURB AND SEVERE ICING. DURING THE UPSET/DESCENT BOTH ENG'S FLAMED OUT AND THE CREW'S ATTEMPTS TO RECOVER THE AIRPLANE WERE UNSUCCESSFUL DUE TO CONDITIONS IN THE CELL. CREW RECV'D AN IMPROPER BRIEFING FROM FSS AND RPT'D THEIR RADAR WAS MALFUNCTIONING TO THE DEP CONTROLLER. SIGMET AND AWW INFO WAS NOT GIVEN DURING THE BRIEFING. AS THE AIRPLANE CAME OUT OF THE BOTTOM OF THE CELL AT 4,000', THE CREW OVERSTRESSED THE AIRPLANE CAUSING THE LFT MLG DOOR TO SEPARATE AND HIT THE LFT HORZ STAB WHICH SUBSEQUENTLY SEPARATED IN OVERLOAD. IMPACT WAS 82 DEGREES NOSE DOWN. NATURE OF THE AIRPLANE RADAR MALF COULD NOT BE DETERMINED.