I'm not too sure with virus, i never get them with my Mac
But if you think the file is not totally gone after uninstall, try
going to Program Files and remove the who file for that software
you installed
Also, Norton Antivirus is TOTALLY useless if you do not update your
antivirus signatures often. If it is outdated, it cannot detect any
new virus on the net.
Btw, best is try to avoid any antivirus downloads from the net as
far as possible. They are usually programmed by not-to-qualified
programmers and even if they are not virus themselves, they can
still easily screw up your computer