My suggestion is that it's a terrible idea to try and run a database server and a domain controller on the same machine, but that's a different argument.
As for correcting it, have you tried connecting to it via the self-assigned IP that's displayed?
Is this server also running DHCP?
It sounds like the static IP might be improperly configured in the network settings. FMS does not "self-assign" an IP address, it grabs it from somewhere in the system, which would point to improper network configuration of your server, which has changed significantly when it was switched to a domain controller.
Try hunting through the network settings to see if you can track down where that secondary IP address is coming from.
Also, have a talk with this admin that's going around randomly promoting boxes to domain controllers without talking to you first (sorry, those types irk me, I'm a planner more than a reactor...)
I can get to Admin Console in a session on the local machine using the correct static IP, but not from any other machine on the network
This suggests that the server is correctly listening on your static IP, and that the self-assigned IP in the Admin Console may be a red herring. Windows Server self-assigns several addresses, including a self-assigned IP (thanks to Bonjour), some IPv6 IPs if enabled, VPN service IPs, etc. The result is that the machine will have several IPs in addition to the static IP you care about, but the FileMaker Server Admin Console will only show one of those, even if it's listening on all of them.
Be sure to check Windows Firewall. In the course of promoting the server to a domain controller, the firewall settings may have been reset to defaults, depending on the procedure your domain administrator followed. Are those ports still set to allow traffic?
FileMaker Server port numbers: http://help.filemaker.com/app/answers/detail/a_id/12120
80, 443, 5003, and 16000 are the ones you need open to remote clients.