i dont know waht can be your problme, but you can try this:
-Try to use FBX instead OBJ.
-Things you can do to check the object:
Export the object to fbx, and try to import again in blender, to see if everything is ok.
You can try to import in another program too, like marmoset, and check if it works.
-if you can export to 3ds, is a good way to clear internal problems on the objetcts, then you can import again the 3ds and export in FBX to unreal.
-another thing you can try, create a new box, then attach the object to the box and export again
hope that help