sounds like the speed setting is not working with the shutter, I have an ae1 check what film speed you have it set at. Check and see if it needs a new battery also. But sounds like speed knob is turning on out side with nothin happening on inside. Find a good repair shop that works on older camera's.

The cloth shutter is the AE1's Achilles Heel. I owned one for 20 years and grew attached to it. I had it serviced but they told me that I really needed to take it out regularly and go through the speeds to keep it working properly. Then my pictures started getting vertical orange stripes--the victim of the shutter not getting out of the way fast enough. I chucked it in frustration and got a Canon EF with a Copal mechanical shutter. I love it. I can also use all my FD/FL lenses with it too. Good news is that the AE1 sold by the millions and there are probably plenty of parts around to repair it. Good Luck!

In any case it off to a repair shop.
query the repair facility FIRST making sure they have a parts graveyard availability for "A" Canon series cameras.
It was a shutter speed priority camera if memeory serves me right and one of the first with a cpu "brain" a big advance at the time.
Good Luck!!