It has been my experience that the Application Server will not work without an ACTIVE Windows desktop session. You can run the Application Server on a terminal server, but you will have to have an active Remote Desktop session onto that terminal server. Furthermore, your local Remote Desktop window cannot be minimized. You'll also want to make sure there's no screensaver active on the remote Windows desktop.
This all stems from the fact that the Application Server uses UI automation to drive the SL client. It can't drive the UI if the Windows desktop session isn't active.
I hope that helps. We've been moving away from Application Server as much as possible. Instead, we're injecting data directly into Solomon database tables in an unreleased state, and then manually releasing the batches. I wish the development team would phase out Application Server and replace it with web services.