render textures applied to meshes imported from Blender 2.60.0

Hi everybody! I'm new to this forum. Googled a bit but didn't found an answer to my problem. I'm using Unity 3.4.2f3 and Blender 2.60.0. When I export from blender, I delete all the scene components except the mesh I want to get in Unity, and export as .3ds, only selection. Unity imports the mesh correctly, as an object container with a mesh inside (if it's a single mesh, but let's stay on the simplest example for now). But when I assign a texture to it, it never renders. The object assumes the dominance color of the texture, but never shows the texture on itself, nor in scene nor in game window. And obviously neither in compiled build. I tried all the possible settings in the inspector panel, both selecting the object from Hierarchy and from Project. Nothing changes as far as texture rendering is concerned. Same behaviour and problem if from Blender I simply save the scene in .blend format and put it into my Unity scene assets. Am I forgetting anything? Am I facing a blackhole of Blender either of Unity?