Cannot access WP Dashboard pages

I cannot access most of the admin pages for my WordPress sites. I can log on to the dashboard, but the updates, plugins, themes, and other pages all either generate a 404 error or, for some settings, cannot save changes.

I have 2 sites running on the same server:
http://loveps.ca
http://lovemj.solutions

For the LoveMJ WordPress install we have tried:
– deactivating all plugins
– reinstalling from a backup
– manually reinstalling via ftp
– wiping out the install and reinstalling using Softaculous, which completely deleted the plugins except for askimet
– adding the php.ini file with memory=128mb
– replacing wp-load.php and load.php
– renaming .htaccess

Now that site gives me Internal Server Error 500, while LovePS still has the 404 page not found error.

This is a new problem with sites that were previously running fine – things seem to have fallen apart with the automatic update to 4.3.