As a recent FE owner, I've read about this problem often but it doesn't seem too serious...
Apparently if you have the camera set to Auto mode and try to shoot with the lens cap on, it locks up mirror and hangs. Set it to M90 and shoot... That should solve the problem.
Sorry, I am probably asking a very obvious question: You've said you turned the dial to M90 but did you shoot?
The film lever could be related... Since the mirror is up, the FE might think it's still shooting and block the lever
Hope things turn out well!