Shortly after climb out on an IFR flight plan, the pilot realized that he had a landing gear problem. He diverted to a nearby airport and made a fly-by past the tower. Tower personnel advised him that his nose gear was partially extended. On final approach for landing, the pilot shut off the engine to make a dead stick landing to avoid damaging the airplane. The airplane touched down on terrain 200 yards short of the runway threshold. Examination of the airplane revealed a fractured nose wheel shimmy damper attaching collar.