I had this problem and solved it, but it took a bit of work.
First problem was a popup window telling me that the resolution wasn't optimal, and old games like Z:GI don't like being minimised like that. If you're getting similar popups, you should be able to disable "balloon notification" by right clicking your graphics card control panel in the taskbar. That solved half my problem.
Secondly, I opened up the program properties and selected compatibility mode for Windows XP (SP3), and under settings selected "640x480 resolution", "Disable visual themes" and "Disable desktop composition".
Now you'll probably get another annoying popup to screw things up again, telling you that the color scheme has been changed to WIndows 7 Basic. Click the wrench in the balloon and it'll take you to the notification area icons screen. Change the Desktop Window Manager to "Hide icon and notifications".
Now, make sure to close all background windows, it seems when I have a browser open it can cause problems too.
Restart the game and fingers crossed, everything should work okay now. If the Activision logo movie plays, you're on the right track. :) If not, you could try disabling windows Aero manually before starting the game, and that should fix it.
Post edited August 02, 2011 by ceeker