Technically, China never really conquered Korea - although the small kingdoms of ancient Korea was submissive to the "Great Land" of China, and always (well, most of the time, anyway) tried not to anger China, in fear of getting attacked.
It's just that Korea never had a written form of language so they "borrowed" Chinese characters to write down Korean language. Of course, all Koreans spoke Korean. But as you guys know that Chinese characters are very difficult to learn, especially for commoners who did not attend educational institute. So only the privileged upper class men learned how to read and write. That is until the Great King Sejong and his scholars invented the Korean alphabet, which, unlike Chinese characters, consisted of 14 main consonants and 10 main vowels. So everyone, even commoners, women and children, could easily learn to read and write Korean. I only taught my former co-worker how to read and write Korean in just few hours - granted he didn't know what it meant!
I can't thank King Sejong enough since I really hated learning so many Chinese characters! lol Nothing against Chinese language, but there supposed to be like 50,000 characters and an educated Chinese person knows about 8000 characters. I think I may have learned a few hundred of them when I young and it was so hard to remember even a hundred because they are so hard to write! And I only remember like 20 characters now.