With some browsers and settings, I can't even get the main Google search page or things like Youtube to show up at all, when almost everything non-Google still works just fine.

IIRC at one time search was Google's core competence.

Once I started no longer being able to click on so many things any more, eventually I figured out that it wasn't a problem with my mouse (a $10 problem), all signs "pointed" to it being a problem with Google (over a $trillion problem).

Have reproduce-able details? Apologies, but your post title is kinda non-specific.