For everyone that wishes to play while they fix the errors... google is your friend.
First off, I want to make a warning: You should only do this if you are competent enough not to ruin your internet, and follow all instructions.
Secondly: This should work for almost everyone that isn't able to connect (unless google themselves start having problems, and that would mean the end of the world.)
Thirdly: The google DNS servers are not available to everyone. If they are not available for you, try googling for "Public DNS servers" in your country. See Troubleshooting
Fourthly: You may have to restart your internet connection (completely) to start using this DNS (This is normally not needed
Finally, the website for most peoples problems: https://developers.google.com/speed/public-dns/docs/using
EDITS: I made a few edits on the points, however the general information is still relevant. If you find a DNS server that doesn't work for you, please try another one or wait for it to resolve in your area.
EDIT: This website provides helpful images for people. It is in Italian, but it can easily be translated
Please remember to use the IP's 188.8.131.52 and 184.108.40.206 (if you can)