Introduction
If you have a Windows computer and are using Avast! Antivirus or Security Suite 2015 or higher, or have recently upgraded to the 2015+ version and OpenDNS is not working, this guide is for you.
Solution
A new feature called Secure DNS is bundled with Avast! 2015 and is automatically enabled by default. Secure DNS is a feature that aims to secure DNS on the computer by running it through Avast's known DNS servers. This prevents OpenDNS from working.
1. To allow OpenDNS to work, disable Secure DNS in the Avast! settings under Active Protection (see image below).
Note:
Note with Avast 2017 Secure DNS has now been replaced by Real Site but this feature causes the same problems that Secure DNS causes.
2. Note: You may need to sign in if this option is not available to you. Note that if you do not have the Internet Security suite and just the Avast! Antivirus, this feature is not present.
3. What does it look like disabled?
Like this:

Note:
Security is not impacted while doing this as long as you are using OpenDNS on the network.

Note:
Another option to prevent Avast from bypassing OpenDNS on the computer would be to uninstall the program completely in Windows. It is outside the scope of Umbrella Support to show how to uninstall a third party program in Windows.