There are some other threads on this but they all suck

I've had some success running Empire Earth using D3DWindower. I'm able to get to the main menu and the display doesn't bug out with compatibility errors, and it works nicely until you click on the window (then it freezes).

1). Download D3DWindower, extract, run the executable
2). Add "Empire Earth.exe" (Program Files\GOG.com\Empire Earth...)
3). Right click > Execution options
4). Common > Set the fixed width and height to 800x600, set it to use windowed mode of course, 'show fps' if you like
5). Window control > Set emulate color model, use color conversion, DDraw primary BLT in the options for DirectX1-7
6). Foreground control > Set everything
7). Direct Input > Set use DirectInput, enable OS special key, and relative to window center
8). Click "ok"
9). Fire up regedit and go to HKEY_CURRENT_USER\Software\SSSI\Empire Earth
10). Make sure 'Game Bit Depth' is set to 0x20
11). Make sure 'Game Window Width/Height' are 800x600
12). Make sure 'Wait for VSync' is 0

Close, go back to D3D Windower, click 'Run Program'

esc
esc
esc
'oh wow it works'
click
'...'
ctrl+shift+esc
down
down
down
delete
:(

EDIT: Problems seem related to the mouse input. If I just use the keyboard it's fine except I can't play.