It sounds to me as if the shutter mechanism itself might be slightly bent. It really doesn't take much pressure to bend those delicate things. As to the remote connection socket cover, I've got a T70 and that socket hasn't had a cover on it as long as I've owned the camera.

If you have a good camera shop around, you might want to take it to them for an evaluation. The T90 is a pretty good camera and it's worthwhile to invest in some repair and cleaning. Best of luck!

Perhaps I should have given more detail about the shutter failure on the Canon T90, The Lens does not shut down to the required aperture, (although it will do if operated manually), the mirror does not flip up, the shutter does not operate and therefore the film doed not advance, AND in the LCD window on top of the camera, the arrow pointing to SINGLE flashes after pressing the shutter release.

Other than take it in to a good Canon service center.
The T-90 while the last flagship of the FD accepting lens bodies is a formidible full featured camera.