Are they possibly legacy media (older formats like .avi) that are not compatible with iMovie?
Also, try deleting preferences and see if that cures the problem. To delete preferences open iMovie while
holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects. Possibly you may need to reboot to set
the changes. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
Another thing that you can try is to put your media into a newly created project and see if the media will import into the timeline of the new project.
-- Rich