Or, if you are using the latest version, just right click the avast tray icon, select Program Settings, switch to the Troubleshooting page and check the “Use XML Storage” box.
You may try to open the \data\avast4.ini file and in the [Common] section, change the item Database=ODBC to Database=XML. This could prevent the Microsoft Jet drivers from accessing the database… does it have any (positive) effect?