Hello!
I bought this game quite a while ago, hoping it could replace my barely-working old CD version, but I'm running into a strange input error immediately upon starting the first mission.
I can cycle through Marines just fine, I can set them to overwatch, can open the map etc., but if I try to give them an actual command (walk, shoot) or end the turn, nothing happens and the game appears to freeze, sort of. I can still continue to cycle through Marines, for instance, but nothing actually happens. If I give a walk-command, action points are subtracted and the first frame of the walking animation starts, but that's all. The game is therefore unplayable right now.
I've tried different resolution settings and compatibility modes on the GOG-shortcut, but neither have worked. Anybody know how to deal with this?
I'm trying to play this on Windows 8.

Looking through this forum, I found Kuchenmann's description of what I believe to be the same issue: http://www.gog.com/forum/warhammer_40000_chaos_gate/is_this_the_version_that_finally_works/page2

Strangely and happily enough, the bug no longer occurs for me. I can't tell you exactly why it no longer happens, except that I tried restarting my computer and also recently installed some Windows updates, leading to further restarts. The game - or at least the first few rounds of the first mission - run very well now, so... solved, I guess?

This isn't very helpful to Kuchenmann or others with this problem, though. Maybe the issue is something as simple as a lot of processes and stuff running in the background? I have taken to playing the game only very shortly after a restart and with little else running. That appears to work.

I doubt it's just that in itself - maybe some particular processes, programs or tools are at fault, but I couldn't tell you which - but perhaps simply restarting your computer and not opening a lot of additional processes will help some of the other people who have encountered this issue...