According to the specs that I can see online, weight is not an issue. Your problem is dimensions. I can't see the package dimensions so I don't know if it will exceed the standard allowances of hand carry luggage. Failing that, you have to look up the "free" allowable dimensions for it to be checked in. I don't think a 27" monitor will have a box whose dimensions exceed the usual allowable for checked in luggage. Worst case you get to label that as "oversized" luggage and they just charge you money for it.
When bringing the product back, together with all the gifts/souvenirs that you are bringing back, you have the standard tax-free allowance. Exceeding that it should just a matter of paying taxes. Now if your other stuff contains food/fruits, that will be a completely different story with lots of traps and gotchas.
Edit: http://www.koreanair.com/local/na/gd/en ... g_0101.jsp
That said, confirm again just to be sure, but try to find out the monitor's package dimensions.
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