As others have pointed out AA77 was hijacked between 0851 and 0854 and it crashed at 0837. Your flight time is off by at least 12 minutes.
Indianapolis ARTCC had simultaneous total loss of radar return and communication. By the way it went "missing" and was suspected crashed over Ohio, not Kentucky.
It was only "invisible" for 9 minutes. The reason it was "invisible" was because the preferred coverage Long Range Radar site for the radar sort box in which it was flying had only a secondary surveillance radar which requires cooperation from an aircraft transponder.
An aircraft with a deactivated transponder can be tracked on Primary Surveillance Radar which works by receiving a radio signal bounced directly off the hull of the aircraft. However Air Traffic Controllers can only see such returns if their Primary Radar coverage is turned on, and if the Radar Data Processor is sending primary information to their screen.
If you have primary coverage available where the transponder is turned off the controller can simply flick a switch and the primary return will immediately appear where the secondary return previously was. Then you can continue to closely track that primary return and keep track of the aircraft.
However if the transponder is turned off in an area without a primary feed, the primary return cannot be picked up. This is what happened with AA77. When AA77 reappeared on primary radar it appeared in a place no one was looking for it, and promptly entered another ARTCCs airspace.
By now, of course, the aircraft could be anywhere, and controllers turning on their primary radar coverage are faced with dozens of primary-only returns on dozens of different screens. There's no way to work out which is AA77, and no way to track every single primary return at once.
At 0908 Indianapolis ARTCC contacted the USAF Search And Rescue Coordination Centre at Langley Air Force Base and reported that an American Airlines 757, flight 77, was suspected crashed in southern Ohio. The SAR centre is responsible for coordinating all search and rescue efforts inside the United States. A Search and Rescue mission was immediately activated to look for the crash site.
At about 0920 Indianapolis ARTCC learned of the other hijackings in Boston and New York airspace, and immediately reassessed the status of AA77. At 0921 Indianapolis ARTCC notified the national Air Traffic Control System Command Centre (ATCSCC) in Herndon, Virginia that they suspected AA77 was a hijacking, and may be heading east.
The ATCSCC immediately told Washington ARTCC and Cleveland ARTCC to start looking for AA77 on primary radar, as well as Dulles TRACON.
At 0932 Dulles TRACON detected a fast moving low altitude primary-only radar return heading east within 6 miles of the White House.
AA77 did not enter restricted airspace at any time during its journey.
AA77 flew past neither the Capitol nor the White House. The section of the Pentagon that was hit was called Wedge 1, and the impact area crossed diagonally so that the exit hole was just across on the very edge of Wedge 2. On the morning of 9/11 Wedge 1 was 85% occupied and Wedge 2 was 40% occupied. Approximately 2,500 people were in the immediate impact area.
Osama Bin Laden chose the Pentagon as a target because it was symbolic of US military power.
The White House was initially proposed as a target however Mohammed Atta concluded after an aerial recon that it would be too difficult to hit due to its small size and the surrounding geography. United 93 was intended to hit the US Capitol Building.
The flight path of AA77 was determined by the Flight Data Recorder which is incidentally what this thread is about. The FDR records aircraft altitude as well as rates of ascent and descent.
AA77s final flight path was tracked by Potomac TRACON (usually referred to as Dulles TRACON) which takes primary radar feeds from a number of ASR-9 radar sites. The ASR-9 is a short range primary surveillance radar that does not have height finding ability.
AA77 did not dive 7,000ft towards the Pentagon in the last moments. It descended 6,300ft over a period of 3 minutes and 18 seconds before descending a final 2,000ft in about 30 seconds.
The FBI was in possession of a total of 85 videos that FBI Special Agent Jacqueline Maguire determined might be relevant to the FOIA request for videos of the impact of AA77. Of those:
56 did not show the Pentagon building, the Pentagon crash site, or the impact of AA77.
16 showed the Pentagon building but neither the crash site nor the impact of AA77.
12 Showed the Pentagon building and the crash site, but only after the impact had occurred.
1 Video showed the Pentagon building, the crash site, and the impact of AA77.
Maguire states that she did not find any evidence that the FBI were in possession of a video taken from the Sheraton Hotel. Videos from the Pentagon security gate camera (which showed the actual impact), from the CITGO Station and from the Doubletree Hotel were released.