A FAA Flight Standards District Office inspector contacted the NTSB investigator-in-charge, and reported that he had received information about an unreported accident at a remote off-airport site. He said the information indicated that an accident had occurred about 30 days prior, and that the airplane was still at the accident site. The inspector traveled to the site, and confirmed that the airplane was there, and that the left wing and left wing spar were damaged. The inspector also reported that the airplane had substantial damage to the fuselage and firewall. The inspector said he returned to the local airport where the airplane was usually kept, and spoke with a certificated aircraft mechanic familiar with the accident. The mechanic identified the pilot, and told the inspector that the pilot attempted to takeoff from a frozen lake, but hit a crack in the ice. The mechanic reported that the airplane nosed down, striking the propeller and left wing on the ice. He also reported that the pilot had one passenger. The inspector reported that he made contact with the pilot, but the pilot refused to cooperate with the investigation. The pilot has not responded to any NTSB requests for information.