I just upgraded my server since I needed to rebuild my PHP/Apache to include a missing library. CPanel makes this easy, however they allow only a few versions of PHP to choose from. The earliest available was still after my current version. I decided to go ahead anyway. Everything worked fine for all my web sites except one. That web site was running Moodle 1.9. When I went to that web site I got the mystersious "Error 324 (ERR_EMPTY_RESPONSE)" error.

Six hours later (might be a slight exaggeration) I finally found the problem. The culprit was the following line in lib/setup.php:

  raise_memory_limit('96M');    // We should never NEED this much but just in case...