Fatal error: Call to undefined function wp_get_current_user()

That’s a problem with compatibility with one of few plugins. Try to deactivate them all, then activate one at a time, and see which one breaks the site.

There are many ways to deactivate all plugins, my preferred one is to update the MySQL database, the table wp_options, record active_plugins. Save it’s old value somewhere, and replace with this:

a:0:{}

—
Видимо есть проблема с одним или несколькими плагинами. Попробуйте деактивировать их все, и затем активировать по одному, пока сайт не сломается опять.

Details:

In my case the guilty plugin calls the function “current_user_can” at improper time.

You case could be the same – most likely, it calls current_user_can() right from the constructor, rather than from a method, which has to be called via add_action (‘init’, …).

It might be something new to WP 3.8 – at the time the plugin is being constructed, the wp-include\pluggable.php had not been called yet, and the function wp_get_current_user is not being defined yet.

So it’s up to the plugin’s author to fix that.