imovie speed button greyed out

You need to select the clip before the speed button will become active. The speed button may be grayed out because you have selected a still image rather than a video clip. You cannot adjust the speed of a still clip because there is no frame rate to adjust. Instead, you adjust the duration of a still clip.

-- Rich

In addition to what Rich said, you can right click on a video clip and choose show speed editor which will give you a button at the top of the clip which you can drag to change the clips speed. If following Rich's suggestions and showing the speed editor do not work I would delete iMovie preferences by opening iMovie while holding down the command and option keys and choose to delete preferences in the dialog which opens.