Redirect loop in ,,,/wp-admin

We recently moved a website from a Godaddy multi-host to a linux dedicacted server.
The site migration itself went ok, the website works fine (for a normal visitor at least).
However, the login to the wordpress admin (website.com/wp-admin) has a redirect loop.
The error is the following:
Firefox: The page isn’t redirecting properly
Chrome: This webpage has a redirect loop

When surfing to website.com/wp-login.php the login screens shows as it should. I can log on but when I do so it redirects me to website.com/wp-admin which has the redirect problem again.

So it is impossible to get to the wordpress backend.
I did some research and found several solutions to this problem, however none of these actually helped.
FYI, these are the solutions we tried so far:

* disabling all plugins
* removing/editing htaccess file
* permalink clean up in the database
* contacting the host but they say it’s because of a problem of the website, not because of their server.
* migrating the backup again (same result)
* replacing all wordpress files/folders (except wp-content)

I am without options now. Anyone has experienced this issue???