Did you install the game in the Default Folder?
e.g. "C:/xx/Ground Control II"?
As I found out a few minutes ago the game cannot find its files if there are spaces in the folder name.
Try renaming the folder to "Ground_Control_II", you also have to change the shortcut to get this to work.
Renaming the folder and setting the gcii.exe to Win. 95 via the compatibility options and starting the gcii.exe as admin via the context menu, that opens up when you right click it, made it work for me. Note that just setting the exe to run as admin via the compatibility settings is not sufficent. Also you have to remove all USB hard / DVD drives.
edit: It turns out that the game still can not always be started this way. I had some success restarting my machine and trying it again after going through the processes described above.
I am on Windows 10 64-bit.
I don't recall having any Problems on my old Win. 7 64-bit system but maybe this helps someone.