In an email sent to a Federal Aviation Administration (FAA), Aviation Safety Inspector (ASI), by the student pilot, he reported that the experimental seaplane experienced a partial loss of engine power during takeoff about 400 feet above the ground. The student pilot stated that he turned the experimental seaplane toward the lake but as he ran out of "speed," he "pitched it to the right into some trees." A postaccident examination of the engine by the FAA ASI revealed that the fuel supply line to the forward carburetor was cracked and leaking. The cracked portion of the line was about ½ inch outboard of the carburetor fuel intake fitting. The airplane sustained substantial damage to the empennage when it impacted trees. The student pilot did not return the NTSB Form 6120.1 Pilot/Operator Aircraft Accident/Incident Report as requested. ADDITIONAL INFORMATION The FAA ASI stated that the experimental seaplane does not have an airworthiness certificate, operating limitations, registration certificate, or any logbooks or record of maintenance performed. He also stated that there wasn't evidence of a current annual condition inspection. The student pilot was not endorsed to act as Pilot in Command (PIC) for single-engine sea airplane or any other aircraft at the time of the accident.