You know, stopping all web access would be fairly effective in defeating web-borne malware!
I don't use "Pro" but I have clients that have used it for years and haven't 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 it's all I can think of right now.
Good Luck.