After takeoff from a lake, the pilot of a Quicksilver Sport 2S experienced a loss of control while joining the traffic pattern. The pilot had just started a shallow right coordinated descending turn when he encountered a "loss of resistance" in his right rudder pedal. The aircraft then yawed to the right. He attempted to correct with the application of left rudder pedal but there was no response. The pilot reduced power, applied full left aileron, and full up elevator in an attempt to arrest the descent. The airplane then impacted the water in a nose down attitude damaging the right float, right wing and right side of the fuselage. It then spun around to the right, and came to rest on the surface of the water. The pilot and passenger exited the cabin and approximately 5 minutes later the airplane sank.