Thanks for answers!

I have tried the following:

Saving the file from Sketchup as a .DAE-file.
Imported DAE to Blender, looks ok,
Exported file as .OBJ, looks ok but renders bad.
Opened .OBJ in poser, looks ok, but renders just like the 3DS-file did.
Tried "normals forward", same result.

Seems like a problem with the .DAE-file, the other apps don´t understand what´s up and down on the mesh-surfaces?
Anything else I can try? (I´m not very good with meshes) :-)