Not every nasty that gets on your PC is a virus.
Many are malware and spyware which some anti virus products dont find.
And the point Rojash was making about letting someone in through the front door is that if you visit a web apge and it downloads some malware or spyware then you have in effect "let it in the frotn door" by visiting the web site.
And no, it is nothing to with you removing Norton.
It COULD be the nasty software has been on your Pc all the time and has just "woken up".
Suggest you download and run the free version of Malwarebytes. This will tell you if you have any spyware or malware on your PC.
http://www.malwarebyt...cts/malwarebytes_free