Thank you for that.
Now that we know your system files are okay, the next thing to try is a clean boot should you have something installed that it doesn't like.
Right click on the Taskbar and select Task Manager then under the Start-up tab click on each item and select Disable.
Click on File/Exit then go Start - type msconfig and press enter then under the Services tab check the box to Hide all Microsoft services.
This is a must before then clicking on Disable all - Apply - OK - Restart and then try the update again.
If that is successful then go back into msconfig and check the Normal startup button and after the reboot you may get an error message which could ID the conflicting item or a program may not work as it should.
If that doesn't work, the only other thing that I can think of would be to perform a repair install.
This doesn't affect your personal stuff or installed programs but you will need a 1607 install disk.
If you haven't got one you can create one through -
http://windowsiso.net/Hover over Windows 10 ISO then over Windows 10 AU 1607 and click on Standard.
Scroll down to your language - Danish I think and select x86 if using a 32 bit system and x64 if using a 64 bit system
Select Save on the download and that should save it into your downloads folder.
You can then use Windows USB/DVD Burner Tool to create either an install DVD or USB. -
http://wudt.codeplex.com/When you open this program, click on Browse then on your Downloads folder, click on the ISO and then on Open.
Insert and select the media you want to use and follow the prompts.
There are a series of commands that can sometimes resolve update problems but as you've already run the update repair in Windows Repair, I don't think they will work for you.
The program has already removed the files from the SoftwareDistribution folder but it won't cause any harm renaming that one to .old.
It's up to you if you want to run them or not before you perform the repair install which is done the same as you did when trying to manually update.
These are the cmds which you can copy & paste en bloc to the cmd prompt where they'll auto run except perhaps for the last one where you will need to press enter.
net stop wuauserv
net stop cryptSvc
net stop bits
net stop msiserver
ren C:\Windows\SoftwareDistribution SoftwareDistribution.old
ren C:\Windows\System32\catroot2 catroot2.old
net start wuauserv
net start cryptSvc
net start bits
net start msiserver
