THE PLT CALLED FROM HOME AT 0909 FOR AN IFR CLEARANCE WHICH BECAME VALID UNTIL 0930. HE SAID HE NEEDED 15 MIN TO GET TO THE ARPT. THE CALL ENDED AT 0914. THE CHIEF PLT PREFLIGHTED THE ACFT WHILE THE PLT WAS ENROUTE TO THE ARPT. THE PLT ARRIVED BETWEEN 0920 & 0925. AFTER ENPLANING & LOADING, HE MADE AN IMMEDIATE START & TAXIED A SHORT DISTANCE TO THE RWY.THE CHIEF PLT NOTED THAT APRX 2 MIN HAD ELAPSED FROM THE ENG START UNTIL THE TAKEOFF ROLL WAS STARTED. UP TO 3 MIN WAS NEEDED FOR THE GYRO TO BE UP TO SPEED AFTER THE GENERATOR HAD BEEN SELECTED. WITNESSES STATED THAT THE CEILING WAS BETWEEN 20-100 FT & THE VISIBILITY WAS REDUCED BY FOG. THE ACFT TOOK OFF AT 0930. AT 0934 NOTIFICATION WAS RECEIVED THAT THE ACFT HAD CRASHED. IT IMPACTED 1.75 MI NORTH OF THE ARPT IN ABOUT A 30 DEG NOSE DOWN, 90 DEG LEFT BANK ATTITUDE.NO PREIMPACT FAILURES WERE FOUND. THE CHIEF PLT STATED THERE WERE NO MECHANICAL DEFICIENCIES ON THE PREVIOUS FLT, BUT HENOTED THAT SOME AVIONICS HAD BEEN SLOW TO WARM UP. ALSO THAT THE PLT HAD PREVIOUSLY USED THE COPLT'S HSI DURING TAKEOFF.