On April 1, 2011, at 1545 eastern daylight time, a Cessna 310F, N6781X, registered to a private individual, incurred substantial damage to the fuselage after the nose gear collapsed during landing rollout at Sanford Orlando International Airport (SFB), Sanford, Florida. The certified flight instructor (CFI) and his private pilot-rated dual student were not injured. The instructional flight was conducted under the provisions of 14 Code of Federal Regulations Part 91. Visual meteorological conditions prevailed and no flight plan was filed. The flight originated from SFB at 1500. The CFI reported that after takeoff, while retracting the landing gear, a loud “bang” was heard. It was assumed by the CFI that the noise came from the landing gear doors closing into each other. The gear-up light illuminated indicating that the landing gear were retracted and the doors were closed. The flight returned to SFB for two planned landings; first a touch-and-go and then a full stop. On the first landing; the gear were extended and a gear-down light illuminated. A touch-and-go was conducted without incident. Upon extending the gear for the second landing, the gear-down light failed to illuminate. The landing gear were recycled, and the gear light gave a gear-up indication. Another gear extension was attempted, and a gear-down indication was not received. The CFI contacted the SFB tower to request a low fly-by for a visual inspection of the gear position. The tower controller reported all three gear were down and the airplane was cleared to land. The touchdown on the main gear was normal; but as weight was applied to the nose wheel, the nose gear collapsed. The airplane was examined by a Federal Aviation Administration (FAA) inspector under the direction of a NTSB investigator. The airplane was raised using aircraft jacks to take the weight off of the wheels. The nose gear shock strut trunnion assembly remained in the compressed position. Approximately one inch of the strut trunnion surface was visible. An attempt to retract the nose landing gear was unsuccessful, due to the strut fork assembly coming into contact with the nose landing gear door attachment brackets. The nose strut trunnion was manually extended out of the cylinder until approximately three inches of the piston surface was visible. The nose landing gear assembly was then manually raised up into the wheel well area and fully retracted. The nose landing gear strut trunnion reservoir was checked for air pressure and was totally empty of air. The strut trunnion reservoir was checked for fluid which was found to be very low. There were no signs of fluid leakage around the nose landing gear strut trunnion. A review of the maintenance logbooks did not reveal any prior discrepancies with the nose landing gear assembly.