The pilot had earlier, at 2111, executed a missed approach following an ILS approach to the Arcada Airport. The weather at that time was sky partly obscured, 100 broken, 1-1/2 miles in fog. He also canceled IFR. At 2137 he called Arcada Radio and advised they had 'a couple of dead VOR's,' and would like a DF steer to Arcada Airport. The pilot had earlier acknowledged that he was aware that the Arcada VOR was out of service. He was provided DF service to a point 3 miles southwest of the airport, and cleared for the ILS RWY 32 approach. No further transmissions were received. The airplane had collided with a stand of redwood trees 4,500 feet northeast of the airport on an approximate heading of 097 degrees. Witnesses stated that the airplane passed over their homes at a very low altitude. One witness stated that the visibility was about 1/8 mile in fog. The pilot's blood alcohol level as tested at the time of his hospital admission was 0.14 gm%.