Robert,
Thank you. Running TestComplete as an administrator is (surprise) not an option. However, I was able to change the setting you suggested. Unfortunately, it required and administrative account to do so. The error was something along the lines of: "Your system administrator has blocked this program...". The message was in reference to the tcManifestUpdate.exe program in the TestComplete bin directory.
I haven't done lot of testing this out, but the hanging problem seems to have gone away with the setting change.
Can I talk you in to sending me an email telling me exactly what registry settings is/are changed by disabling the "Windows Store Application" option? I will need to write a justification for changing that setting on a long term basis for my testing team in order to gain approval from our system security organization.