I don't have a very uncommon machine:

Intel i7-4790K on ASUS Z97-A
MSI GeForce GTX 1070 GAMING X 8G
16 GB RAM

The only unusual thing is the 21:9 ratio monitor with QHD (3440x1440).
Game crashes at startup.

I am using the non-Galaxy version.

Update 02MAR2018: The Steam version of the game is working perfectly on the same machine.

Update 23APR2018: I found the cause of the crashes. It's because I routinely denied the game any contact to the internet by blocking it with my firewall. Without the blocking it works. But I still must ask the question: Why must a DRM-free game from GOG in the classic version without Galaxy and without ever touching any multiplayer-functions talk to some dubious servers via the internet? That really sucks.

What kind of crash are you experiencing?

I bought the steam version and I crash on startup. from what I gathered on another post, it was starting to sound like a certain Windows Update was required. My crash is "Battlezone Combat Commander has stopped working" immediately after launching the game.

http://steamcommunity.com/app/624970/discussions/0/1694914735999829312/

Could you try all solutions in this post here, please? (ignoring the verify integrity step as it's a Steam thing)

If they don't work please follow the steps here:
http://steamcommunity.com/app/624970/discussions/0/1694914735999829312/

Minus the steam name

Glad you guys found the windows update I needed:

Problem: Windows 7 and cannot find video drivers.
Solution: Ensure this update is installed:
• Win7 32bit https://www.microsoft.com/en-us/download/details.aspx?id=26767
• Win7 64bit https://www.microsoft.com/en-us/download/details.aspx?id=26764
• KB: https://support.microsoft.com/en-us/help/2533623/microsoft-security-advisory-insecure-library-loading-could-allow-remot

The update definitely fixed the issue for me. Thank you!