When I click on the "Run Analysis" command I get a message saying "Fatal Error: Cannot Start Analysis Engine."

This is caused when STAAD.Pro is not installed with enough administrative privileges.

If you are getting this message, when you try to analyze any STAAD file, uninstall the program through the Control Panel. Delete any associated STAAD folder that might be still present (for this version only), check the All Programs group to make sure none of the short-cuts is left behind.

Once, all these have been checked; reinstall the program. For Windows Vista/7/8 machines, right-click on the executable file and select the option "Run as administrator", though you are logged in as the administrator. This ensures that the program is installed properly.