Page Not Found updating 3.9.2 to 4.0

Hi and thanks in advance. I am in way over my head.

In trying to update from version 3.9.2 to 4.0, I keep getting a “page not found.” This is happening when I click on the Please update now link, as well as Updates, Plugins, or Appearance in the menu.

This is occurring on multiple sites. Two of my sites are running Headway theme (3.7.7 and 3.7.8), and WP 3.9.2. (A third, less-used, site, running Pilcrow theme, allowed me to update from WP 3.5 to 4.0, but gives me the same page-not-found error when I click on Updates or Themes.)

My web host, InMotion Hosting, was helpful in trying to sort this out but were not able to resolve the issue. They have referred me back to WordPress, with what they believe are “premature end of script headers.”

They suggested that I may have missed an update between 3.9.2 and 4.0, but from what I can tell there were no other versions in between.

Normally I would try to change themes and/or deactivate plugins, but I can’t access those pages.