I noticed that my Internet Explorer can't access any websites and my email (Eudora) connection is timing out.
Which version of avast are you using?
Into the firewall settings (if you use any besides XP SP2 internal one), the following programs should be allowed to connect:
C:\Program Files\Alwil Software\Avast4\ashWebSv.exe (avast! Web Scanner)
C:\Program Files\Alwil Software\Avast4\ashMaiSv.exe (avast! e-Mail Scanner Service)
C:\Program Files\Alwil Software\Avast4\Setup\avast.setup (avast! Update executable)