This fixed the majority of my problems as well.

I can get in game now, but I'm still trying to figure out why the screen stops refreshing when I select certain buildings to construct, then freezes completely 20 seconds later.

My Setup is Windows 10 with a Core-i7-7700 and a Geforce 1060 with 6GB and i had the same Problem with a Freezing game in the Menu.

What worked for me, was installing without GOG-Galaxy, using the compatibilty mode for Windows 7 as an admin and changing the grafix to my Geforce instead of primary driver and Direct3D Hardware TnL with a resolution of
800x600x32.

I disabled all renderers and grafic effects, but maybe it would work with them enabled. I dont have the courage to try, after i finally got the game working.

You are also able to change the settings with regedit under "\HKEY_CURRENT_USER\Software\SSSI\Empire Earth"...

Hope you get your game working...

So here is a 3 year update. The game still does not work. i have friends and family who have the same game and it works on their window 10 pcs. I have found that the problem my computer is having is a low-level engine dll error. I believe it is graphic card based but not sure. I have done everything from installing with antivirus off to updating drivers etc. I cannot seem to find a fix for this issue. Also i can't change my graphics card's hardware acceleration. I don't if this new information sheds like on anything but there is where i am at.

In case the other suggestions do not help:
Disabling the MSI Afterburner (Riva Tuner Statistics Server) Overlay ( for Hardware usage and such) solved the issue for me.
No other tweaks or compatibility settings needed.
So it might be worth disabling this or any other overlay that might be running in the background.

Thats what mine was doing. The only thing I worked out was to run in win 7 mode and play around with the ingame resolution. I found higher resolution makes the game crash. I tried this as my previous pc was win 7 and I never had a problem running it on that. I settled on 1920 x 1080.

EE1. I got it working with compatability mode win7 and then setting the game resolutiion to 1920 x 1080. Also in 3d acceleration I set the it to direct3d to stop the curser showing the blue square. I had to restart the game for this to take effect.
Hopefully my experimenting might help someone.