There's a problem with the Wayback Machine in specific which can kill your ability to access it quite silently, unless you know how to use the browser's development tools and interpret headers.
It has to do with cookies: Somehow, the Wayback Machine sets cookies... and sets cookies... and keeps setting cookies, until it overflows its own ability to accept cookies. At that point, your browser tries to access a Wayback Machine page, handing the server all of the cookies it currently has, and the server refuses to deal. It absolutely denies everything, sending an error header and a blank page. You have to clear all web.archive.org cookies to get anything at all, at which point it works perfectly.
I've completely solved this problem by blacklisting web.archive.org in browser cookie blacklists. I haven't had it happen since then. As far as I'm concerned, the problem is diagnosed and just needs to be solved. At their end.