Hi there,
Thank you again for the quick reply. I appreciate you providing this information and trying all of the steps that I have asked you to! I checked our Officejet 8600 with the same CM749A model number and it too has the most up to date firmware version (CLP1CN1322CR) and it has the option for Korean under Preferences and Language. I definitely feel at this point the issue is simply with the printer that is right in front of you, so it would be best to call HP Tech Support for your area and inquire about an in warranty replacement. If the printer is out of warranty there won't really be anything they can do other than assisting you in choosing a suitable upgrade.
Again, thank you so much for your time and effort and I hope you have a wonderful day!!