downloading and installing El Capitan is not going to help
The usual cause of this problem, assuming that the rest of the internet is working as expected, is fat fingering the address (URL)
How are you trying to get to YouTube and Google News? If you are using some sort of short cut then stop doing that and enter the URL into the Address line by hand.
If I enter youtube.com into the address line it takes me straight to YouTube, try it and let us know.
Are you using anything like Little Snitch, an app that has the ability to block outgoing connections to specific websites?
I am trying to get onto YouTube and Google News; Using Safari, Firefox, Explorer, and Google Chrome how ever, I get a message that says the "server not found". This is only for these two websites and I can access everything else without a problem. I am running OSX on my MacBook Pro. I haven't downloaded El Capitan; will it help to download it? I don't think downloading it will solve the issues.