Forum Discussion
We have a build guy who deals with this stuff, so I've never been involved directly, but you may get some helpful suggestions here:
http://stackoverflow.com/questions/17955554/running-automated-ui-tests-as-part-of-ci
... your options sound like they'll depend on the version of TFS you're using. I see TeamCity mentioned in there. That's what our build guy was using to trigger my automated tests .... which required an active user session/GUI.
I decided to mark as solved, since the problem described in the title and my first post are solved, and the "new" issue seems to be TFS only rather than having to do with TestComplete:
TFS can not even deploy the test agent on the build PC without me having an open remote desktop connection, saying "The job has been abandoned because agent XX did not renew the lock. Ensure agent is running, not sleeping, and has not lost communication with the service."
Thanks to everyone who contributed here.