My Nikon FE has this annoying fault where the shutter occasionally fires at ¹⁄₉₀th of a second regardless of setting. I don't have enough money for a new FE (I'm 14) and I was wondering what could be causing this.
1/90th of a second is the limit of the cameras shutter speed with out electronic assistance. On your shutter dial you should see it listed as "M90", the "M" standing for mechanical.
My first course of action would be ensure that you're using a fresh battery, then check the battery connections is free from corrosion. If the problem persists, it might mean there is a more serious fault with the camera's electronics.