kubadachi: I tried turning off the UAC and running as administrator, but it still wants the CD. While I do have the CD, this should be fixed. I have tried contacting GOG, but it seems like an endless circle of "read this article" and I still cannot get to an email address or form to ask for help. Does anyone know the way to contact them because all of the "Contact Us" links do not get to them, just read this form/article.
Just a small observation: If you are looking for help, it might be a good idea to tell your audience what you are talking about - "game" is not very specific. Looks like some people guessed right, "game" = "Morrowind" as it seems, but I wouldn't rely on this happening every time.
In many cases a problem like you describe it occurs because of a second installation of the same game, or because of an incomplete de-installation. For example, there is a bug in the de-installation procedure, or it was terminated / canceled before it was finished, or the user simply deleted the game folders without using the de-installation procedure. As a result, game entries remained in the registry, which may influence a new installation of the same game.
If you know what you do, you can clean the registry yourself (not advisable for inexperienced people), otherwise it may be difficult to get rid of the undesired registry entries. Sometimes it helps to de- and re-install the game, hoping that the de-installation deletes these registry entries. In your case I may have tried to uninstall Morrowind (GOG version), then install the old CD version, uninstall it, and finally re-install the GOG version. Cumbersome and time-consuming, I know.