I see WP-Super-Cache there and doing its job, and your site responds instantly most of the time. Then all of a sudden it hangs.

It's probably a bad Apache configuration... you're allowing more workers/threads to spawn than you have RAM to run on that system, and a high KeepAlive timeout (15 seconds) tying them up on connections that aren't needed anymore.

If you configure it right, Apache on an old box with little RAM can easily handle HN-level traffic for a static site (which a cached blog is).