On my keyboard the shortcut is "한/영" button (there are two additional buttons on Korean keyboard). If I press this button, the language is switched to Korean, but only "?"s are typed. I'll try to test on WinXP.
I can select Korean characters from drop-down panel, but I cannot type them (if I type '권', it should be typed in 'ㄱ'-'구'-'궈'-'권' sequence, but just '?' is shown). Is it by design?