That's it. I'm starting over.
I could not convince the application server install to finish completely. Add to this the fact that I was now getting an error when trying to shutdown the database server, and an error when starting the application server. Time to start over.
This time, I am following the install instructions to the letter right from the start. That was my big mistake last time. I was forced to install certain things out of order. It possible that since I installed SQL Server 2005 before installing IIS, something just wasn't right.
So, I've now reinstalled the database server. Windows Server 2003, IIS, all critical Windows Updates, and SQL Server 2005. Easy as punch.
I am in the process of reinstalling the application server. I'll get the domain controller thing right from the start this time, so that might go a lot smoother.
Disclaimer The opinions expressed herein are my own personal opinions and do not represent my employer's view in any way.