This is what I do and it works fine:
1) Download .zip from GIT
2) In cmd go to extracted GIT directory and type: "python install.py" (this requires Python)
3) Download windows dependencies 7zip and extract only ENIGMAsystem and ENIGMA.exe (.jar's should already be there because of "install.py")
If you don't have python then extracting .jar's from 7zip should also work. Are you sure all the paths is correct? Like is the ENIGMA.exe in the main directory, lgm16b4.jar also in the main directory and so on?
edit: Ok the problem is the windows dependencies 7zip. The included .jar's are not up to date and don't work with the newest ENIGMA. It doesn't compile the compileEGMf.dll and so crashes. Try these:https://dl.dropbox.com/u/21117924/ENIGMA_newest_jars.zip
I downloaded them via the install.py. Extract and overwrite the ones you have. Then run again. Wait until it finishes compiling (should show up as "Done" in console).