I do feel like I'm in airplane and I can't pop my ear pressure correctly, which results in impaired hearing, plus the stuff coming out of my sinuses could be used in a Ghostbuster movie, very easily.
Anyway:
One aspect that is glossed over in the installation guide for Office Project Server 2003 is that by default (at least when I installed it on our server), it does not populate the user tables with accounts from Active Directory automagically.
Normally that wouldn't be a problem, but I was thinking that it wanted my AD account information when I was going to the Web Access portal. Nope. It was looking for the username 'Administrator' with whatever password you assigned it on install.
On our domain, Administrator doesn't really exist (the SID does - but the actual name is renamed - security thru obscurity - I know, I know) so it was of course the last thing I tried.
So, save yourself some time and learn from my mistake - don't assume it is looking for AD credentials when you try to log into the Project Server. The error message was unfortunately not much help. It told me to ask the system administrator for help. Well, I can ask myself all I want, I still didn't know.