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I am having precisely the issue described by the thread author. However, neither switching to Direct 3D TnL or running as an administrator has helped the problem.

Interestingly enough the game runs 100% fine on my laptop with the same OS.

WARNING! NeoEE completely broke my game after complaining about the lack of CD keys. After uninstalling NeoEE again, it still left files laying about on my installation folder!

Intel i7 4790K
AMD Radeon R9 290x
Windows 7 Ultimate
Post edited November 19, 2015 by NodCommander
I had this issue (game freezing shortly after loading a random map, or when changing the graphics settings), but found a fix:
For me, the problem turned out to be a shader conflict with my newer graphics card. We can force a program to use a different shader technique using the free 3D_Analyze program below:

Once downloaded and installed, right click the program and change the compatibility to windows 7 AND check run as an administrator.

Run the program, and open the Empire Earth executable to edit it, then select the checkbox for "Force Max. Pixel Shader v. 1.1", then run the file to see if it works. If the problem is fixed, repeat the process but save the patch as a batch file, so you don't have to use 3D analyze every time you want to get EE running.

Good luck!