The pilot reported that during the take-off run the aircraft was not accelerating very well due to the soft wet surface. At about 70 knots the pilot raised the nose in an attempt to get the main wheels off the runway to allow the aircraft to accelerate in ground effect. The pilot said that as soon as the aircraft lifted off it veered slightly left and was about to settle onto the ground again, so he closed the throttles and tried to maintain directional control on the ground. The aircraft entered mud and grass to the left of the runway for about 200 metres. The nosewheel then broke off, the propellers struck the ground, and the aircraft came to rest in about 8 metres. The passenger who was an engineer, had previously run the left engine as it was suspected to not be producing full power. No fault was found with the engine. During the accident takeoff the engineer had noted that the left engine was performing normally.