The pilot of the Cessna 310R stated that he and his passenger departed from Waterloo Airport (ALO), Waterloo, Iowa about 1800 eastern daylight time, destined for Lake Placid Airport (LKP), Lake Placid, New York. Prior to the flight, he checked weather conditions via the Internet for the visual flight rules flight. After takeoff, the pilot requested flight following from air traffic control (ATC) for the route, and it was granted. About 2 hours before the estimated arrival time to LKP, the pilot made contact with Lansing, Michigan Flight Service and requested a briefing. During the briefing, the pilot was not provided with the notice to airmen (NOTAM) regarding a closed runway at LKP. Throughout the remainder of the flight, the pilot was in contact with several different ATC centers. The pilot terminated the flight following from Boston Center when he was 20 minutes from LKP. Prior to terminating the flight following, he listened to the Saranac Lake Airport automated surface observing system to determine local weather conditions. About 12 miles from LKP, the pilot keyed his microphone on LKP’s common traffic advisory frequency to bring the runway lights on. The pilot located LKP’s runway 14 when he was 10 miles out. During the approach and landing, the pilot did not notice anything abnormal. Seconds into the landing rollout, the airplane encountered several gaps on the runway. The airplane came to a stop on the left side of the runway, incurring damage to the landing gear and fuselage. The pilot and passenger were able to disembark the airplane without assistance and were uninjured. The responding Federal Aviation Administration inspector stated that the runway was closed and under construction. Several sections of the runway’s surface were removed. There were eight flashing markers in the middle of the runway and cones with an "X" marking at the approach end of the runway. The "X" marking was not lit and the runway’s lighting system was not deactivated.