Another issue recently, with a different site.
The host supplier had moved the site to a new server and apparently this has “Suhosin” installed. This is an advanced protection system for PHP installations. It was designed to protect servers and users from known and unknown flaws in PHP applications and the PHP core.
It can also kill your WordPress dashboard (and the rest!).
I could authenticate successfully and get the WordPress banner menu showing above the site, but if I tried to get to the dashboard or any other part of WordPress administration, I was being redirected to the 404 Error page.
The site continued to work fine, I was just unable to change it in any way as I could not get to the dashboard.
A quick chat session with the host supplier and they disabled Suhosin. Now all is back to normal.