BUT
- the Virus Alert icon remains blinking Red and Green
- and from time to time a window "Your computer is infected / critical system error" appears.
This doesn't appear to be an avast alert, it doesn't have a green and red virus alert only the standard pop-up very noisy alert. A screenshot of the alert would help.
I believe this is likely to be some scumware ad (possibly Windows Messenger, not MSN Messenger) trying to get you to download the solution to your problem and when you do you are likely to have more problems to contend with.
Shoot the Messenger, Windows Start, Run, type services.msc and click enter. At the Services Pop-up, find Messenger, double click it and if Messenger is running, click Stop, once stopped, select Disabled in the Startup type: and finally click OK.