My first observation would be this: The behaviour you describe is normal for Windows NT/2000 operating systems, and is not something "wrong" with your particular machine, per se. All NT/2000 machines, both server and workstation, will boot as far as the login screen and then wait for human interaction.
The main question here is this: What is running on this server that is inaccessible if someone is not interactively logged in? All NT services will start upon boot-up even if a user does not log on. If you have an application running on this server that requires an interactive logon, you have a few options.
a. Use a third-party utility or the NT Resource Kit's INSTSRV.EXE and SRVANY.EXE to convert the executable into a service that can be started, paused, stopped, etc., like any other NT/2000 service. If you are in an Active Directory-enabled environment, you can also investigate using Group Policy to create a startup script (as opposed to a login script) on your servers.
b. DISCLAIMER: This option should be used as a method of the ABSOLUTE LAST RESORT, as it has the potential to create a LARGE security liability on your server (I wouldn't even bring it up, because I hate it just THAT MUCH, but it IS an option available to you if you absolutely cannot find another way to do what you need to do.): Configure your servers to automatically log in at startup. This involves a registry hack, the instructions for which can be found at http://support.microsoft.com/default.aspx?scid=kb;en-us;Q310584. All usual disclaimers regarding registry editing apply, and the security implications of this option must be SERIOUSLY considered before implementation.
This was first published in June 2002