You can't navigate the main menu using the keyboard, btw, that's not something the game lets you do - so that specifically isn't an issue.
Hmm. The fact that escape/enter works means that most likely keyboard input in general is fine (since those are the only two keys the main menu would respond to anyway), and that the problem is with the mouse not registering clicks.
I can't think of anything that has changed in the game as far as that's concerned, and that fullscreen vs not makes a difference also makes it seem like something system-related. Are you able to test whether the previous version of the game *currently* has this problem on your system or not? If it doesn't, that might narrow it down to something about how the game is being run, though I'm not sure how that'd help, though it'd be an interesting data point.
Also: if you run the game in dev mode (data/config/settings.json, set devMode to true), you can press 1/2/3 in the main menu to instantly get into a couple of quick test missions. How the game behaves in those (i.e. whether you can fire using the mouse etc) might point us in a useful direction.
Also: did you happen to get a new mouse and/or install new mouse or other input drivers recently? I seem to remember something like that causing an issue a while back, though I can't find the thread.
It's as if it's somehow partially losing focus?
That might be a possibility, actually! Depends on what else you've got running in the background; sometimes other programs will do that. Might also run a virus check just to make sure it's not something malicious...