My advance film lever no longer has any tension. It doesn't advance the film. It just flaps around. Does this mean I stripped or broke the plastic gear?

Do you have a film in the camera? If so is it all exposed? Best thing to do is press the film rewind button and try the lever at the same time - this will eliminate stuck film issues as it removes film tension from the system. If this does not solve the issue then you need someone to have a closer look.

Your camera is in cocked position with shutter fully cocked and that is why you cannot advance the film advance lever. Set the shutter to x position ( on your shutter speed dial on the right hand side and top of your camera ) . The shutter should release and then you should be able to advance the film advance lever.

Did you impact the top cover? Spill something on the advance lever?Try putting some Windex on a toothbrush and cleaning around the advance lever and see if that frees it up

This is a known fault with this retro model, I'm afraid - over time, the plastic gears get worn, and eventually fail. Solutions are mentioned on the Pentax Forums.

A Canon AE-1 is not an EOS camera the Canon "A" series is manual focus while EOS is auto focus. First thought In answer to the advance lever stuck or jammed I'm going to assume the camera is in serviceable condition and has not been subjected to water damage or harsh use. If we are dealing with just the advance lever then I'd say that you have over advanced the film at the last frame. I've done this myself after loading a 24 exposure and thinking I had a 36 exposure film. At the bottom of the camera there is a little pin which releases the advance lever and allows the user to rewind the film. Under normal conditions when it's time to rewind the film into the canister this pin offers little resistance to pushing in to release, however depending on how much force the advance lever has been subjected to increases the tension on this pin. Push the pin in and rewind the film.
Second thought is if you have film in the camera and it has not been used fully then it's possible that the film has already been advanced to a new frame and the shutter needs to be activated before the lever will become free and advance to the next frame.
Other problems with the Canon "A" series cameras is they have a tendency to dry out the lubrication and begin to squeak when the shutter is fired. This condition can eventually result is a shutter seizure and give the same advance lever condition.
Those are the three things that come to mind over this lever problem lets hope it's just run out of film.

first make sure the rewind button is not stuck down. open the back door and rotate the advance sprocket back and forth to release the button. if that did not work take the bottom cover off and check the white plastic gear near the take up shaft. if that gear broke it will have to be repaired by a camera repair person.
there are no new parts for this model so get a cost estimate first.

You probably need to take the camera in for repair. It sounds like the film transport is not connected to the shutter/mirror cage ***'y.

plenty of these cameras are on ebay sold for parts

I removed the advance lever cover as suggested and tightened the screw. This did not solve the issue. However, I then realized the film rewind button on the bottom of the camera was stuck on the "in" position. I could not get it to release which meant I could not advance the film lever to free up the shutter. To solve this issue I removed the bottom cover from the camera (taking out the 3 small screws) and then pulled the advance lever button all the way to the right. This released the button that had been stuck in and allowed me to advance the film lever properly again and take more pictures. Hope this helps!

Yes this is fairly common with K 1000 and the Spotmatics : although the shutter is cocked and hence you cannot advance film you cannot release shutter because mirror box is not cocked. Remedy : remove bottom cover and locate mirror box lever which protrudes slightely and is movable up and down and is spring loaded. Move upwards until it licks in position ( moving up against spring tension ). Now release the shutter and camera should let you advance the film .