It just keeps downloading the same 4.4 GB over and over. It takes 50 min each time and when it's finished it starts to download again. It try to pause it, but it mess up everything so I can't start the game or download mods!

Have you installed steam from the disk ???

You can uninstall steam, and download steam from the homepage. -> http://store.steampowered.com/about/

Yes, I installed from disk, but the Steam client gets updated on the internet so it can't be the same Steam now that I had on the disk.

I know. My intention was to tell you, NOT to install the disk steam client at first place.

Just delete everything related to skyrim, and steam.

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First do a standard uninstall. (Control Panel\All Control Panel Items\Programs and Features-> Uninstall The Elder Scrolls V: Skyrim)

Next, delete your skyrim folder under C:\Program Files (x86)\Steam\SteamApps\common\

Then delete your Skyrim directory under Documents\My Games

Then under C:\Users\[Your Username]\AppData\Local\ - Delete the Skyrim folder that is in it.
(You should enable to see the hidden files under windows to delete that folder.) HOW: (View - Options - Folder Options - View - Advanced Settings: Show hidden files, folders and drives)

Go to your Steam folder. Delete the folder named appcache. (Important)

After uninstall steam completely. !!! (from Windows control panel)

Use Ccleaner after all this (http://www.filehippo.com/download_ccleaner), Go to the Registry tab and hit -
In the Options tab go to Monitoring and uncheck: Enable System Monitoring and Enable active Monitoring

Reboot your computer (Important)

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Install steam client from the homepage: http://store.steampowered.com/about/

Let it run, update and then install Skyrim.

Well, it seemed to solve it self. I will look into your suggestions if I get trouble with it again.

Obviously something related to steam.