THE ACFT COLLIDED WITH THE GROUND IN A NEAR VERTICAL NOSE DOWN ATTITUDE AFTER BEING OBSERVED BY WITNESSES TO PITCH DOWN DURING CRUISE FLT. THIS ACFT & PLT FLEW EARLIER IN THE DAY WITH AN INSTRUCTOR WHO HAD TO RECOVER CONTROL OF THE ACFT AFTER THE PLT ALLOWED IT TO ENTER AN UNCOMMANDED SPIRAL. THE RADIO TRANSCRIPT OF THAT FLT CONTAINED, 'PROBLEMS WITH THE HSI WE, AH, NEED TO COME BACK.' THE PLT HAD BEEN SCHEDULED TO GO TO LOUISVILLE BUT THE FLT WAS CANCELED. LATER THE SAME DAY THE PLT/OWNER RETURNED TO THE ARPT, SAID HE HAD READ ABOUT THE HSI SYSTEM AND WANTED TO RESET IT AND FLY. SHORTLY INTO THE FLT THE PLT RADIOED THAT HIS AUTOPLT WAS 'STUCK IT IS TAKING MAIN STRENGTH TO HOLT IT.' HE SAID HE WANTED TO TALK TO SOMEONE WHO KNEW ABOUT THE BONANZA TO 'SEE WHAT HE COULD DO.' IF THE AUTOPLT DISCONNECTS AN AUDIBLE SOUND IS HEARD. NO SUCH SOUND WAS HEARD ON THE TAPES. AFTER THE ACCIDENT THE TRIM TABS WERE FOUND IN THE FULL NOSE DOWN POSITION.A PLT WHO HAD FLOWN THIS ACFT THE DAY BEFORE SAID THE AUTOPLT WOULD NOT DISCONNECT USING THE MODE OFF SWITCH.