Broken image links in media library after restore

You are on right track buddy.

Now do this.

3. Install plugin called regen thumbnails . Run regen thumbnail. It will take few minutes but after finishing process, you will have all the images in the media library. This plugin basically regenerate all the thumbnail in the media library for all the sizes. Becuase you had very old WordPress. It makes sense directory structure changed since. Try this and I hope it will work.