Widgets and Menus not working, AJAX not loading on admin pages

Thanks for taking a look.

So, I have two websites, and widgets and menus areas, as well some other things are broken.

So, I can add widgets when in accessibility mode, but i can’t drag them in normal mode, nor I can edit/re-order menu items.

What I’ve tried at first:
-Manual upgrade
-Deactivating themes and plugins
-define(‘CONCATENATE_SCRIPTS’, false);
-changing permissions on admin/js files

So I’ve started looking at theme files, and this is what I see in both active theme files, and Twenty Twelve:

[Huge block of encoded text removed]

the code can usually be found in index.php, functions.php and header.php.

Sometimes, it’s just this. Sometimes, this code is on the top, then the “normal” index.php page code.

Also, deleting all themes, then re-uploading just original Eleven Themes doesn’t help.