DURING A NORMAL TAKEOFF THE PILOT EXPERIENCED A DUAL ENGINE FAILURE ABOUT 10 FEET ABOVE THE RUNWAY. THE PILOT STATED THAT HE LANDED ON THE REMAINING RUNWAY AND ATTEMPTED AN 80 DEGREE LEFT TURN ONTO TAXIWAY 'C'. THE AIRCRAFT FAILED TO NEGOTIATE THE TURN AT THE ROLLOUT SPEED AND ROLLED DOWN A RAVINE WHERE THE IT COLLIDED WITH A TREE. THE INVESTIGATION FAILED TO DETERMINE A MECHANICAL MALFUNCTION OR FAILURE DURING THE POST CRASH EXAMINATION. BOTH ENGINES OPERATED NORMALLY WITH THE EXISTING AIRCRAFT SYSTEMS AND FUEL ON BOARD. IT WAS ALSO DETERMINED THAT THE PILOT HAD AMPLE RUNWAY AND GRASSY AREAS AVAILABLE TO SUCCESSFULLY COMPLETE AN EMERGENCY ROLLOUT. BOTH PILOTS WERE CERTIFICATED TO OPERATE THE AIRCRAFT; HOWEVER, THE PILOT IN THE LEFT SEAT WAS NOT INSTRUMENT RATED. THE FLIGHT WAS DEPARTING UNDER INSTRUMENT FLIGHT RULES.