Using windows explorer, navigate to the path given by Tech, assuming you installed avast in the default location. If the DATA\Log\ folder or setup.log file aren't there then you may have a corrupt installation. Not wishing to put words in Tech's mouth, but he isn't saying it is possible to have two installations of avast, just to start from scratch, a clean installation.
First download the latest version of avast
http://www.avast.com/eng/programs.html and save it to your HDD, somewhere you can find it again. Use that when you reinstall.
Now uninstall the existing avast version using the add remove programs, reboot.
Now install the latest version you downloaded, reboot, this will give you a clean install (from scratch Tech mentioned).
This way you have the latest version before you uninstall as outlined above and you will remain protected not having to go on-line without protection.