open a terminal, go to that downloaded blender directory ( cd Downloads/Compressed/blender-2.71-usw). Then you type ./blender and tell us what happens.
That’s weird. You download Blender in your “/home/YOUR_USER” and you try to run the “blender” executable from there. Do not download Blender into another disk or partition, only in your home.
Just in case, you do not use “sudo” for any of this tasks (download Blender/uncompress tar.bz2)