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
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.