I have an AE1, On the AE1 the film counter will continue to progress ( the numbers will keep advancing) from 1 to 38 regardless of whether or not there is film in the camera, if there is no film in the camera you can keep actuating the shutter (after 38 is visible )and using the film advance lever forever.

If you had loaded your film properly (the sprocket holes were captured by the sprocket pins on the advance spool) then the film would advance until all of it was pulled from the cassette. If the piece of tape that holds the film to the spool in the cassette is still attached then film will stop advancing and you will not be able to use the advance lever. if the tape is broken the film continues to advance until it is all on the advance spool and the advance lever will continue be usable. In this scenario If you opened the camera then all of the film would be on the advance spool ( out of the cassette and past the shutter ) and the camera could not rewind the film.

For the winding problem two possibilities. When you opened your camera and saw that the leader of the film was still out of the cassette then either

1- The film was properly loaded onto the advance spool and the film did not advance because of a mechanical issue with the camera or

2- the film was not properly loaded and the sprocket pins did not grab the sprocket holes. ( this is the most likely scenario and is supported by the fact that the counter did not run backwards while turning the rewind knob )

Now for the film not being rewindable by the camera or by hand would suggest that the tape that holds the film to the cassette spool has failed.

I would surmise that you did not expose the film, ( it did not advance in the camera) coincidentally and confusingly, the film cassette was not rewinding properly.

You can do a test clip, go into the darkroom ( no light ) pull out 3 or 4 inches of film and cut it off (leave enough to cut a new leader ) develop the clip and see if there are any images. If the film is not exposed you can open the fuji cassette take the film and load it onto a bulk film re-loadable cassette and use it as normal or shoot the fuji cassette in your camera but you will not be able to rewind it back to the cassette, you will have to take the camera back to the dark room to open the camera, push the rewind button, carefully and straight pull the film out of the camera. develop or put in light tight canister to take to lab.

Or write the film off as a loss open it in daylight and see why i will not rewind. Let us know.