I have a FileMaker 9 Server Advanced installation running since January on the server. Encountered this exact same issue as you described. For me it occurred after a power outage. The issue was driving me up the wall.
I was thinking something in the database server was corrupted so I would have to reinstall it. Having searched the web and not finding much information about it, I was a bit frustrated.
Then I realized I forgot to check the event.log. The log stated that the database server was quitting due to another copy of the server version using the same serial number. D'OH! I had forgot that I installed the FileMaker Server Advanced on my personal computer so I could mess with it. The server computer was looking at my personal computer and saying, "Oh we can't run the database server cause someone is already running it on this network".
So I turned off my personal computer, restarted the FileMaker 9 Server Advanced Admin Console, and everything was fine.
Could this be what happened to you?