murt,
Some suggestions on free firewalls:
Zone Alarm
Sygate
Kerio
AS David has said, you most certainly can get a virus by only being “connected” to the internet. Your computer can be “scanned” by third parties and a virus sent to it. That is what a good fw prevents.
Once you have an FW in place, then run a full Avast scan and remove all viri.
I would also suggest a good anti-spyware program like Adaware or Spybot SD.
Good luck,
Techie