Do you use MS Internet explorer?
It seems that some users have the security settings in Internet Explorer set in such a way, that it does not ask for a password at all, preventing people from logging on! You then get this screen and nothing else.
In MSIE, you can find the secutiry settings in the menu "options -> security". You can then click on "internet" (that is the picture of the globe). If you then click on "custom level", you will get a pop up list with all the security settings. The last one on the list is "User authentication -> logon".
What is that set to? If it is set to "Anonymous logon", you will get problems logging on to this system (or any other that uses this way of asking for a password!).
This setting should best be set to "prompt for username and password". If that is set correctly, you should be able to log on without any problems.
With other browsers, a similar thing might apply, although the instructions above will obviously not apply to other programs. Still, you might be able to find security settings in your browser too!