Am I a Zombie? Spam and Anti-Virus Software

Hi All, we hear a lot in the news of late about folks computers being used for all sorts of reasons remotely without their knowledge to send spam amongst other things.

I often notice my laptop is busy when I initiate a command when connected to the internet, Have I been Zombiefied, how can I check this out. Task manager reveals just the usual processes however I understand that some items can run without registering within task manager. I have, I am told, good anti virus software "Sophos"

The question is how do I find out what the computer is up-to when is tells me it is busy.