I’ve imported some FBX objects (originally they are exports from Unreal Engine just in case this might be helpful) and after I’ve imported them (from one FBX file) in Cycles they stay black. What I’ve checked so far:
- They have the right materials and when rendering in Eeve I also see the materials
- When I add a light to the scene the surfaces show the correct materials - so the objects actually are missing a light source when there is just the environment
- see attached screenshot - the world has a background with strength > 1. Adding HDRI has the same effect: I see the HDRI in the background but not light is reflected from the objects
- face orientation of the objects is also correct. I also tried to add new materials - no changes. The materials are set up correctly
It seems that the objects only reflect lights from other sources then the world. I bet there is one checkbox I must tick but I have no idea which.
Have you checked the ray visibility options for the world material? I could replicate the problem with them:
thank you for your hint… yes, I’ve checked them. Unfortunately it’s not these checkboxes 
And I also checked the face orientation for the objects. Everything’s fine regarding this
I added a camera and made an actual render - same same.
Here you see a shader - to me it just looks perfect. On the left side you see the image editor with an actual image - a missing texture is not the problem.
Additionally I found out that a sun light also does not work. I read in the documentation that when a volume shader is defined for the world the world light and sun lights doesn’t work - but there is nothing defined for a volume.
Waaait a minute… Have you checked that there are not some huge objects in the scene that you are actually now inside of?
Because UE has a different measurement unit, so objects imported from there into Blender might have a 100x scale. That would explain why you can only see world lighting affect the objects in Eevee, because Eevee will have world lighting everywhere also through objects, but Cycles will calculate the world lighting realistically. Also it would explain why sun lights don’t work.
Anyway, only the color texture should be in sRGB, all other nodes should be set to non-color. Also there is something going into specular input, I’m not sure what it is or does it really work in Blender.
You could test does disconnecting it make any difference.
ok, now you are my hero 
I found a suspicious “SkySphereBlueprint” mesh and actually this caused all the trouble. It had a size of 32km * 32km * 32km and after deleting it everything worked.
Man… a whole afternoon and evening of re-installing several UE versions, importing, exporting, checking all the checkboxes… and then it is just a stupid large mesh in the scene… it’s hard to become a 3D artist 
THANK YOU SO MUCH!