Well, if there's a newer compatible version than 335.23, go to that. Drivers are usually worth a shot, but if you're on the latest available to your card, it's obviously something else. (Although you could try reinstalling the driver in case it's become corrupt, but I wouldn't do that as a first resort.)
Do you use antivirus or other security software? If so, please name what you use.
I don't, actually. I used to have AVG but since then I have either uninstalled it or it expired. I'm updating the driver now to something a bit more recent and I'll get back to you on how it goes.
Updated the driver, the image came up immediately after the game finished its check and the menu background loaded up. The "Play Game" button didn't even pop up before the game force quit.