Here's a fix that has helped at least one user. I also tried this myself, confirming that I could duplicate what several of you are seeing, and then could fix it.
First, download this utility:
http://www.bleepingcomputer.com/files/Merijn/bugoff.zipThis is a small security program designed to show you where you might be vulnerable to certain malware exploits, and turn those Windows features on or off.
So, run "BugOff.exe" (which is inside the zip file you downloaded). This will display 7 or 8 protocols and objects that Windows supports, and whether or not those features are enabled or disabled. The second one is "ms-its". If this protocol is disabled on your computer, you can bet this is preventing the TD from functioning. So, enable the ms-its protocol and then try to run the TD.
Is it a security risk to enable the ms-its protocol? Possibly, if you generally use Internet Explorer. This protocol has obviously been abused in the past, but I do not know at this time whether or not this hole has been patched by Microsoft, nor whether or not this exploit is prevalent "out there". It's not a risk to run the Tournament Director, but it could be to leave this protocol enabled while you generally surf the web with IE. On the other hand, I personally wouldn't consider it a higher risk than any of the other security holes that exist in Windows, Internet Explorer, etc. Best bet: use Firefox.
Finally, for the paranoid, you can always use this utility to enable the ms-its protocol before you start the TD, and then disable it after you're done using the TD. (Don't disable ms-its *while* the TD is running, it *will* cause problems!)