According to the pilot, due to thunderstorms along his route of flight he elected to divert to a nearby airport. During landing, the aircraft nose landing gear contacted the runway and the airplane "bounced," which resulted in substantial damage to the forward bulkhead and the windshield center post. According to a Federal Aviation Administration inspector, the pilot had originally been cleared for an approach to one runway and subsequently performed a go-around due to being above a "normal" glidepath. The flight was then cleared to land on a crossing runway, at the tower controlled airport, entered final for the crossing runway, and upon landing the airplane porposied three times before coming to rest. According to the pilot, there were no preimpact mechanical malfunctions or abnormalities that would have precluded normal operation.