What version of iMovie did you use to create the projects initially? Is that version still on your computer or otherwise accessible to you?
Unfortunately iMovie 8.06 is not completely functional on El Capitan and later operating systems. Black frame stills are one of the reported malfunctions. There is no path to update iMovie 8.06 to iMovie 9 or iMovie 10. Therefore there is no cure other than to update your projects and events into iMovie 10 from within iMovie 10 (File/Update Projects and Events). Is that what you did when you tried to "convert" the projects using iMovie 10?
If iMovie 8.06 (or your earlier iMovie version) still works, you can share out your projects to standalone movies. That might work if the still pictures actually are in the project. You can then drag the movies into iMovie 10 as one large clip, but editing would be limited to such things as splitting the clip, deleting, adding effects, adding titles, adding transitions between the splits. Previous edits that are embedded into the movie, such as titles and effects could not be changed unless you can cut out that portion of the clip.
If you can find some way to play the project on your computer, you could make a screen recording of it (Command-Shift-5).
You appear to still have your original media for the older projects, so you always have the option to use the original media to recreate the project in iMovie 10.
-- Rich