OK, get both the removal utilities on the page I linked you to, above.Save them to the desktop. Boot into safe (see below) Run them both, in turn. Then reboot.
Make sure you have the full setup file for the latest Avast 5, direct downloads available
here. This should be available, ready to install, after you have run the uninstall utilities.
Go offline for the removal/re-installation of the AV, because you won't be protected without an AV.
From the horse's mouth,
here is how to restart into safe mode. This mode is for diagnostic and troubleshooting purposes. It is useful particularly for removing components that otherwise might be locked by the OS in normal mode, as they aren't loaded in safe.
Expect the desktop and other options/fonts to look very different. Don't worry about that.