Where can I re-start installing the GalCivII without downloading the 1GB again?

Here is what the problem ist:

I installed the demo version and played with it a while.

I installed the full version.

I deleted the demo version via control panel. But for some reason the TotalGaming folder still holds the demo version and

in the start menu it shows in the Stardock Game Folder the Name of the full version but the link is pointing to the demo version. The situation is now that none of the installations are working.

AND YES, I uninstalled the DEMO version via control panel.

There must be a complete mixup int the registry setting.