Hi Dave,
The first log file that you sent did not have much information that was useful. However, the second .log file does have interesting information. That exception that you mentioned refers to a file (davinci...) that contains libraries for various widgets. All other warnings are also indicating that something is not quite right with installation as it should not be missing files and it should not be trying to re-install them.
GUI Composer can run in any directory that is writeable. Would you be able to try installing it in a new directory e.g. C:\testgc ? I would suggest trying 6.1.1 or 6.2 runtime. The key requirement is that the application be copied to that webapps folder.
I am speculating that uninstalling/re-installing may have left some old files in C:\ti\guicomposer that are affecting GUI Composer this way.
Thanks,
Martin