by Ken Task.
Suggest going into settings for the course and in Appearance, set theme to Force Boost.
There is no direct link to backup in 4 (dumb IMHO, but this is a 'new and improved user interface') and using 'Course Reuse' should display a pick list left top of the courses to choose to other actions (defaults to 'import'). Click the drop down list and you will find what you want to do ... backup.
Just in case that didn't work, use URL line of browser to go to:
/backup/backup.php?id=112
where the id number is the id number is your course ID number.
Probably a good idea to turn on debugging all the way to developer and see if moodle is showing something there (before the 404). If it doesn't then, check web server error logs for clues.
I also saw in your screen shot of the 404 error screen a grayed out 'Activate Windows'!!!! What the heck is that about and could that be a reason for 404? Dunno... don't use Windows myself.
'SoS', Ken