The pilot took off in VMC conditions from an airport that is on the coast. The surrounding mountains a few miles inland had been obscured by clouds and low ceilings for several hours. About 15 minutes after takeoff, the pilot contacted an approach control facility to request visual flight rules flight following. About one minute after that first contact, the pilot started giving indications that he was having problems with the weather and with finding his exact position. Within about 3 1/2 minutes after the initial contact with the controller, the pilot said that he couldn't see 'anything'. That was his last known radio transmission. His transponder squawk code disappeared from the controller's radar screen at about the same time as the last known transmission. The controller asked the pilot several times if he was VMC or VFR. The pilot responded affirmatively every time. The aircraft collided with a mountain at about the 3,300 feet level.