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I hit F12 in game, but no screenshots are taken. The option to view screenshots in greyed out in the game's drop-down menu in GOG Galaxy. But strangely, FRAPS also doesn't take a screenshot, though F12 is the key for it.

Any ideas?
I seem to recall there being a issue with Galaxy's screenshots on the General Discussion forum. I don't use it myself though. Can you check if it works for other games.

If not, DOSBox itself has a built-in screenshot capture. Ctrl+F5 by default.