t-p on "404 pages and inability to update anything"

404 indicates failure to communicate with the server.
- it could be configuration issue
- it could be memory issue
- it could be permalinks issue, review this : How to fix 404 error when using Pretty Permalinks?
- it could be optimization issue
- it could be a conflict with plugin: try resetting the plugin folder
- it could be a conflict with theme: try switching to the default theme for a moment via FTP and see if that resolves the issue.
- check for .htaccess file presence and check if the default wordpress mod-rewrite code is there or not. There are times when .htaccess file is not writeable or gotten deleted - Check the server error log for your hosting account. Ask your hosting provider for assistance to locate them.