A recent update to the theme used on one of our sites and others caused a problem with WordPress. Unfortunately HTTP 500 errors are notoriously difficult to pin down.
After removing all of the plugins and the site still threw HTTP 500 errors, we then turned to the theme to attempt to get the site to load.
With no theme, the site came up empty but the admin settings do not require a theme to work. We then installed a fresh copy of the most recent version of the theme and now the site is rendering properly.
We hope that this experience will not be repeated but we have faced problems galore with the site mostly as WordPress is so heavily customized for users. Errors are usually uncommon but they do popup.
We suggest minimizing the number of plug-ins to reduce the chance of failures. Updates are usually tested but problems can still slip through.