I just had a blue screen of death. I had a battle pop-up message like you and clicked yes to confirm it and nothing happened, no battle. Clicked to attack again and same thing. Saw I still had 3 moves left, moved the ship and tried again. No go. I then tried another ship and tried to attack. Same thing, nothing happened. Then I got the BSOD.
"Not sure what info I can grab for the developers."
You can send in the debug file located under: your user name/my documents/my games/GalCiv3/. The file is called "debug.err".