I don't know how all of that stuff works - but here is the Google help pages - you might find the answer there.
http://www.google.com/support/websearch/?ctx=web



[We got hit by GreenAV this morning at about 1am. All I did was log onto Firefox and bingo it started to download. We managed to block it (while being a bit hysterical) with Avast. But I wonder if it followed one of us from another website, just when we closed down the internet a few hours before?]

was the computer still on the whole time, but you were both logged off, or was it shut down /turned off?

I think if it was on the whole time in between uses {vs a complete shut down} and even though no on was actively using it - the green AV must have got started the first use and then when you went back online it popped up and tried to continue..
just my theory on how it could have came alive so quick as soon as you started up Firefox.

you might look through you cookies list and see what isn't needed - I just looked at mine and lots of junk that I was surprised to see.
Firefox lets you customize more on the cookie settings now so maybe play with those??