To say a plane became "invisible"because it turned its transponder off is fantasy.
You need a quick lesson in US radar.
First off, there's two main types of radar. The first is called "primary" radar. This is the traditional radar method of sending a radio signal into the air and monitoring the "reflection" after the signal bounces off the physical hull of an aircraft.
The second type is called "secondary" radar. This involves a transmitter sending out a signal which interrogates the transponder carried by an aircraft. The aircraft's transponder then responds with certain information, depending on the mode being used (unique transponder code, altitude, heading, etc).
In the United States the FAA operates a series of radar sites to cover the air traffic flying over the country. Primary radar coverage is provided by Primary Surveillance Radars (PSRs). Long range Air Route Surveillance Radars (ARSRs) provide feeds to FAA ARTCC centers while smaller Airport Surveillance Radars (ASRs) provide feeds to TRACON and ATCT facilities.
Secondary coverage is provided by the ATCRBS (Air Traffic Control Radar Beacon System) which consists of transponders on aircraft and beacons on the ground. The beacons are mounted on PSRs and turn with them, however (and this is important) not every radar site has a PSR - quite a few are "beacon only" sites that only provide secondary radar coverage. For example, of the nine sites feeding to Indianapolis ARTCC, only six have primary radars.
In the United States all aircraft flying in Controlled Airspace above a minimum altitude are required by law to carry an operating transponder. As such the FAA relies almost exclusively on its secondary radar network. During normal operations primary coverage is turned off, and only secondary returns are displayed by the Radar Data Processor - a computer that filters radar information.
Using a switch, the controller can turn on their primary coverage if the need arises, however they need to have a reason to turn it on.
To fully understand what happened with AA77, it's important to understand how radar is displayed on a radar screen.
Although a given airspace receives signals from multiple radar sites, the RDP doesn't display everything. This would cause chaos as the radars are turning, and thus each would paint a given aircraft at a slightly different time, and therefore at a slightly different place, producing a double image (or even triple image!).
So instead, airspace is divided into "sort boxes" which measure 16 miles by 16 miles. Each sort box is assigned to the closest radar site, and when the RDP receives signals for that airspace it ignores everything except the feeds from the radar site assigned to that sort box. Thus any given area of airspace is covered by exactly one radar site only.
(There's also back up sites assigned to each sort box in case the preferred site is offline at the time, but that's not relevant to this discussion).
The problem here, of course, is that the controller cannot see the sort boxes, they have no idea which radar site is feeding which part of their screen, and they have no control over it. They see a single uninterrupted picture.
Now, in the case of AA77, by sheer bad luck it was flying in a sort box assigned to one of Indianapolis ARTCC's beacon-only radar sites when it was hijacked. As such, when the aircraft vanished, it totally vanished from the system. No doubt the controller immediately turned on their primary coverage, but since the radar site assigned to AA77's airspace had no primary coverage, the contact for AA77 did not appear.
So with total loss of communication and transponder, the controller rightly concluded the aircraft had suffered some sort of catastrophic break up. They knew nothing of what was happening on the east coast, and indeed it would be another ten minutes before the second attack, and a half hour after that before the FAA would know that coordinated terrorist attacks were under way.
While AA77 was in this dead airspace it turned around. Despite your assertions that AA77 turned for Washington DC before its transponder was turned off, you're wrong on that count. AA77 made a slight course change towards the south prior to transponder loss, but it didn't make its full turn until afterward. As such controllers were searching for AA77 to the south and west of its last position, and that's where they expected it to reappear on primary radar if it hadn't crashed.
By the time anyone realised it was a hijacked aircraft and might be headed back east, it was long gone, just another needle in the haystack of civil aircraft filling the sky.
Now, as for military radar...
The FAA has a number of different models of ARSR, the newest of which is the ARSR-4. It's the only primary radar that has height-finding capability, although this isn't actually used by the FAA.
The ARSR-4 sites are located around the perimeter of the USA and form the Joint Surveillance System (JSS). This network provides radar feeds to both the FAA and NORAD. This gives NORAD a degree of primary radar coverage over the USA, however not sufficient to see where AA77 was hijacked.
The ARSR-4 feeds are sent from the radar sites to the various FAA facilities where they are processed and displayed on screens. Another feed is sent from the FAA facility to NORAD's three Sector Operations Control Centers (SOCCs) known as WADS, NEADS and SEADS (NEADS and SEADS have since merged into EADS).
The problem begins with how each organisation uses their feed.
The FAA uses primary radar only as a back up - in fact as early as the mid 90's the FAA were pushing hard to scrap primary radar altogether and only the military protested about it. A few months before 9/11 the FAA had actually started the process of preparing to shut down the primary network all together.
For NORAD, however, primary radar is their key tool. Their concern was detecting infiltrating enemy aircraft coming in low over the water, trying to avoid radar contact. Obviously these enemy aircraft would not have transponders. They'd be small, they'd come in low and fast, trying to be invisible. As such NORAD turned up the sensitivity on their radars as high as it could go so they could detect every single little radar return.
Now this was well and good for aircraft coming over the water, but it had repercussions on the landward side - it made their radar totally useless.
The reason is ground clutter.
Ground clutter is noise on a radar scope as a result of the radar signal bouncing off objects near or on the ground. This can include buildings, trees, and even insects in the air.
Over water, where NORAD was interested in looking, there's virtually no ground clutter, so they could turn up the sensitivity without a problem. But on the landward side, over the eastern seaboard, the ground clutter was enormous, and effectively made it impossible for them to locate anything.
This is why, although the FAA were able to track AA11 on primary radar, NEADS could not locate the flight.
And
that is how a plane became "invisible" because it turned off its transponder.