Well, as you've discovered you can't just unplug a domain controller. It has to
be demoted.
I just dealt with this the other day. There are two specific articles I came across
that had all the information I needed to remove the dead domain controller from the
working domain controller and active directory.
Unfortunately, I don't remember the process and I don't remember the articles.
However, I can say that I found all the information by looking in the event viewer
and googling the errors, then reading the documentation you will find about improperly
removed domain controllers. Your event logs will be full of errors.