The pilot reported that the autopilot was inadvertently engaged while taxiing to the departure runway. The pilot and his passenger attempted to disengage the autopilot by depressing the "A/P" button on the unit's control panel. The pilot reported that there were warning buzzers sounding as they attempted to disengage the autopilot. The pilot eventually turned off the avionics master switch in order to completely power down the autopilot. After he reestablished power to the avionics, the autopilot appeared to be disengaged. He then contacted the control tower for a takeoff clearance. The airplane "prematurely" rotated and became airborne during the takeoff roll. The pilot stated that he immediately aborted the takeoff, but "struggled with elevator control because of a significant nose up pressure." The airplane landed off the left side of the runway, impacted a snow bank and another runway before coming to rest nose down. A post-accident examination of the airplane showed that the nose landing gear had collapsed, causing substantial damage to the engine firewall. The two-axis autopilot system had servos that controlled the elevator and elevator trim positions. The elevator trim was not in the takeoff position, with the indicator showing a nose-up trim setting of about 8/10 of its total travel. No anomalies were noted during an operational test of the autopilot system or after a download of its fault log. The autopilot was installed with the correct software version and was in compliance with all required airworthiness directives. The pilot reported that he had minimal experience with the use of an autopilot and that he had not received training on the autopilot system installed in the accident airplane.