Cant watch various website videos, such as yahoo news clips

I assume (since you didn't state it in your post, but this is where I'm seeing this issue) you're using IE11.

YouTube is almost finished with updating everything to HMTL5 (MP4) which doesn't require Flash Player. They use javascript to detect if a browser has Flash Player or not, and if it isn't detected, it displays videos in HTML5. Yahoo hasn't done this yet, or if they have, it's not to the extent that YouTube has.
The reason that's relevant is what follows. 

This is a known problem with Internet Explorer 11, which Microsoft has been aware of since October 18 when they released their latest "untested" browser. The pages can't recognize the browser, so they don't recognize any of the plugins, like Flash Player. So far, Microsoft has made NO indication that they have any plan to fix it soon.
Microsoft's recommendation is to use Compatibility View for affected pages, and "pretend" you're using an different browser. Trouble with that is it has seen limited success at best, and you have to individually enable it for EVERY page that has problems.
I'm not big on "pretending" so I recommend actually using another browser.

Firefox (from Mozilla)

Opera (from Opera)

Safari (from Apple)

Chrome (from Google)

ANY of those will work where IE11 won't, with the Flash Player Plug-in (For all other browsers), and Chrome doesn't even need that because it has its own Flash Player plugin built in.