The pilot stated that after takeoff the flight proceeded IFR towards the destination airport (The Florida Keys Marathon Airport), Marathon, Florida. He cancelled his IFR clearance, and performed the pre-landing checklist. While on the base leg over water during the dark night, he became distracted by the failure of the landing light. With the landing gear and flaps extended for landing but the power set to 15 inches of manifold pressure, he did not recognize the airplane was descending. When the airplane impacted the water he thought they were at 1,000 feet. He also stated that he attempted to activate the runway lights using the common traffic advisory frequency but stated he could not see them. In hindsight he stated that he must have been too low at that time to see the runway lights.According to the County of Monroe Assistant Director of Airports, the runway lights at The Florida Keys Marathon Airport come on automatically at night and remain on "step 1." Being a 14 CFR Part 139 airport, a complete night inspection is performed each Friday and Monday, and each working day in the morning a continuous inspection is performed on the runway lighting circuit. As noted in the Daily Self Inspection Reports, the airfield runway lights were functioning properly during the course of the weekend and there were no issues with the runway lighting system. The runway end identifier lights for runway 7 were out of service at that time.