Virus problem

When I boot up my pc my recycle bin icon is replaced with a duke nukem head. I’m running Norton AntiVirus 2003 Pro with the most updated pattern files and have done a full system scan on both of my computers. On the other one there are small red dots in the bottom left hand corner of the icons. Is this being caused by a virus, and why isnt norton picking it up? If its possible that there is a virus, are there any programs that would catch any kind of virus that I could use to ensure a virus free system? Thanks.