Purchased Avast Antivirus Pro and installed it and immediately all DNS resolution stopped. I turned off Real Site and the Web Shield thinking that might fix things but it did not. Did an update and rebooted. No luck. Is the new best way not to get viruses simply to shut down all web access permanently? 
Sigh. I didnāt look at the most likely cause as I figured ānahā¦ it wouldnāt have done THAT.ā
Wrong. It definitely removed both DNS entries from my network adapter. WHY WOULD YOU DO THAT AVAST!?!? Unbelievable.
You know, stopping all web access would be fairly effective in defeating web-borne malware! ;D
I donāt use āProā but I have clients that have used it for years and havenāt had this issue.
This is strange.
Are you getting those via DHCP from your router (not static/manual)? Might try cmd ipconfig /release and then ipconfig /renew. In fact ipconfig /all might shed some light on it.
Was there an option at installation for creating a proxy of some sort or a VPN option?
If you set manual entries for DNS in the properties, do the settings change or disappear?
I hate guessing but itās all I can think of right now. :-\
Good Luck.