Lesson for today: read the install instructions.
Well, as soon I a stuck the Team System DVD into the drive, the install instructions came up. They are excellent - well written and helpful. I just wish I saw them earlier today.
So it turns out I missed several important steps.
* Both the application and database server needs to have the Application Server role configured. The application server needs ASP.NET while the database server does not. Neither server uses Frontpage Extensions.
* I had to download all the Windows Updates. There were a lot (22).
* I had to download and install SharePoint Services 2.0. Then had to download and install the Windows Update for that.
* I had to download and install ADAM (Active Directory Application Mode). I'm currently stuck, as the install instructions appear to require ADAM running on a specific port number, but my server says that port (SSL) is already in use.
Anyways, it's way past my bed time. I'll have to tackle the rest of this tomorrow.