It sounds like a virus and/or spyware. Working on other people's computers regularly, I can tell you without hesitation that Norton is the absolute worst thing you can possibly put on your computer to "protect" it. What it will protect it from is excessive performance, as it damn near takes the machine over with all kinds of stuff running in the background. Either take my word for it, or hit control-alt-delete on a machine running a reasonably modern version of norton. You won't BELIEVE all the processes norton has running in the background.
To boot, their antivirus program is far from the most effective at catching viruses. Yes, I know-you pay for it and it looks professional and pretty. Thing is, there are free programs out there that catch more viruses than norton while imposing far less of a performance penalty on the machine. As already mentioned, avg is one of them. Another (and the one I use) is antivir. BOTH are far better than norton, and don't bog the machine down with a bunch of dumb shit.