My Canon A2E (35mm!) did exactly the same thing. I'd bet it's a bad shutter. A new one cost about $100 (five years ago) to have installed & should get you working again.
I had about 60,000 pix on my Digital Rebel before I sold it (still working well) & just hit 42,000 on my
Rebel XT. The shutter should be good for 100k+ photos, but things like dirt/sand/beer can cause it to fail prematurely.
Call Canon or visit their web site & ask for a service center that can fix a bad shutter.
EDIT: Hmmm...missed your "fixed it" post.
