I know nothing about Korean language, but I have just installed a Korean keyboard layout to check out your problem. And if I type D K S it will show up 안 character in Word, not ㅇㅏㄴ.
I have Office 2013, but no language packs or proofing packs is installed for Korean. And it works for me.
If you have not done many customizations to your Word 2013, I would suggest backing up and deleting you Normal.dotm template.
It should be in this folder
%appdata%\Microsoft\Templates\
Copy and paste this line into Start search or address bar in explorer.
In that folder find a file Normal.dotm, back it up in my documents or something and delete original. Close Word before deleting. MS Word will create a new file with default settings after you will start it again.