Olddog: Thank you for your comment - indeed, uninstalling AOS was possible as you instructed. In another forum somebody told that addons cannot be uninstalled if the "remove" box is disabled. Such is the case of AOS when looked into tools-manage addons-more information.
Unfortunately, the removal of AOS did not help in getting IE working. Nor did help the extra lines in webshield.ini.
BUT: The unchecking of "Automatically detect settings" in the Internet Options of LAN settings solved the problem as predicted by diego6111 on January 7, 2014.
Now Avast 9.x does not prevent using IE 11 and works beautifully side by side with Comodo 6.x. irrespective of AOS being enabled or disabled.
(ADSL-modem, make D-Link)
In addition, I had a possibility to test another ADSL-modem (ZyXel) in the very same ISP's network. In this case the "Automatically detect settings" could remain checked.
What is the change from Avast 8.x to Avast 9.x to force the unchecking of LAN option's "Automatically detect settings" when IE stretches to internet via a D-Link ADSL modem??