When do shut downs occur? randomly or just while you try to start PC?
Did you do the sfc /scannow command? or try start up repair?
Try a clean boot and see if its any better - this will tell us if its one of your start up programs causing it:
https://support.microsoft.com/en-au/kb/929135
If you all of those, and it still plays up, I feel the best move might be a fresh install if your users still don't work. Copy everything you want to save onto a USB or Onedrive or another hdd (I tend to do all 3). A fresh install will wipe entire hdd C is on so make sure to remove everything before you start.
Download the
Windows 10 media creation tool and use it to make a win 10 installer on USB
change boot order in bios so USB first, HDD second
Boot from installer and follow this: http://www.tenforums.com/tutorials/1950-windows-10-clean-install.html