I think I would start by logging out of the server. You will probably get better results by using the various server tools remotely, or by SSHing in via Terminal.app.
The first three things I would check are:
- Does anything look strange in the Server Admin tool?
- Are any processes that do NOT belong to YOUR user currently pinned?
- If you have another user on the system, does logging in with that user result in the same behavior?
My initial thought is that perhaps something has gone awry with the user account you are using for admin -- and that this might be linked to a server process the user depends upon (such as Open Directory). Applications you run might be trying to get a user-level resource that the system is not allowing for some reason despite its apparent availability, and so they spin up trying to access it again and again.
But this is just an initial thought -- you'll be able to diagnose it much more closely with the three steps above.
Also, use cat via remote SSH to examine various server logs (if trying to run Console.App is not possible due to that 100% spin) and see if one message keeps getting hammered over and over.
From there you can start to triage the issue. Good luck!