Wordpress and Apache2 can handle it just fine. You probably just need to enable caching.
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).