Iphone 4 - Moving carriers in Korea but locked(?)

I have an iPhone 4 originally with KT as carrier. After 2 year contract i got a new iphone 5 and decided to give my 4 to my daughter who is using SKT as carrier (in korea). But after putting in the usim, the phone did not find the connection or carrier... Is this phone factory locked? If so, how do I unlock it? Do I go to the apple support shop or to the old carrier? Please help!