When I press ctrl-alt-del on a particular windows 2003 server, the Username and Password fields are greyed out, so I can't login.
I'm logging in remotely using VNC if that makes any difference, but my colleague has checked the real console and gets the same results.
One common reason is that there is a remote session to the server console which was not shut down properly.
Its usually VNC that causes this. Are you using TightVNC? Try changing to UltraVNC or RealVNC or vice versa.
There are a couple of reasons this could happen. Firstly it could be that 'Log On Locally' has been disabled in a group policy somehow, this would prevent users logging in at the console. As your using VNC to connect you are effectivley using the console. Can you try and connect using RDP and see if you can get in that way.
Another option is that the Windows Logon Service has stopped, which if that is the case you would need to reboot.