The 1,000-hour pilot was conducting a local personal flight. Shortly after takeoff, while retracting the landing gear, the pilot did not receive a gear-up indicator light. After numerous attempts to extend the landing gear, the pilot elected to fly to a local airport equipped with emergency fire and rescue personnel and equipment. An in-flight visual inspection by another airplane reveled the landing gear was not in a down and locked position. The pilot performed a gear-up landing on the runway and the airplane came to rest with the left wing and horizontal stabilizer resting on the ground. Examination of the nose landing gear revealed that the hydraulic line, part number S2178-4-0102, had separated from the fitting to the nose landing gear actuator. Inspectors were unable to locate records on the last hydraulic line replacement.