It was a post from May of '03, I believe. Here's what they posted:
"Open the services console and double click on the fast user switching service. Now click the dependencies tab at the top. Make sure all of the services listed here are enabled."
If you don't know, you access the Services Console from Administration in the Control Panel. My "Terminal Services" dependency was not enabled. Fortunately it was also listed in the Services Console, so I just enabled it and everything worked.
Apparently this is not an uncommon problem from what I saw in the old posts, and there were some pretty convoluted fixes suggested, but this one was the simplest.