I have such object (based on this tutorial):
Does anybody know what is going on here?
Blender Cycles expects Cycles Materials. Blender Render expects Blender Materials. They are not shareable across render engines.
If you replace your materials with Blender Materials then you can use Blender Render. You can try a test by replacing one or two materials. You might want to archive your file or create a different scene to keep the original intact.