Virus Effected Website/My Computer opts to shut down

Confused and looking for a solution

- a week ago I went to a sketchy website and my computer shut itself down, when it restarted it turned out that some kind of virus sent a bunch of spam to everyone on my email contacts list

- I did a full Norton scan and it only found tracking cookies and told me all was safe

- Today I was at a similar sketchy site (not the original one) and my computer told me it's shutting down again to protect itself again; But when I logged on a website I am associated with was affected and now whenever anyone goes on it Google states that it is infected and redirects people away from it

 

What do I do? I'm at a complete loss???

How can I fix this? (and no, I wont go to the sketchy sites anymore - it was a free TV site).

Help.