Hello Nicolas, and welcome to Sysnative!
In addition to the instructions Alex has given you, it would be great if you could help us a little bit by seeing if there's anything you can do to identify what's going wrong on the 40% stall. We'll analyse the data and if we can find a cause we'll feedback that information to Microsoft so that they can potentially create a fix.
So, before you follow Alex's instructions (if you haven't already), can you please try DISM one more time please.
Then, I want you to download this tool from Microsoft:
https://technet.microsoft.com/en-us/sysinternals/bb896645.aspx
and start it up. I then need you to make a few changes:
Filter > Reset Filter
Filter > Drop Filtered Events (so there's a tick in the box)
Filter > Filter, then:
Process Name is dism.exe then Include > Add > OK
Edit > Clear Display
File > Uncheck Capture Events
I now want you to start dism.exe and let it run until ~37%. Then, go back to Process Monitor, File > tick Capture Events > let dism.exe run until 40% and stall for a little bit, then File > Untick Capture Events.
Finally, File > Save > "Events displayed using current filter" (tick in Also include Profiling Events too) > Dot next to Native Process Monitor Format (PML), then click the "..." button next to Path, and save Logfile.PML on your Desktop > OK > OK.
Then, if you could upload that new file from your Desktop to SkyDrive or any other file sharing website, make it publicly accessible and share the link here, that would be absolutely amazing.
Please know that these steps are completely optional. Alex's instructions are what you need to fix your computer. However, it's people like you who voluntarily help us report back to Microsoft with enough information to give them a chance of fixing the issue that allows these rare issues to be sorted out once and for all. I do completely understand though that everyone's busy at this time of year and you're probably up to your eyes in work right now. So it is completely optional.
Thank you so much.
Richard