Lets see if i know some more:
Drama City: What Should I Do? / ep.234 /2004 / Lee Jun Ki /
http://en.wikipedia.org/wiki/Drama_City:_What_Should_I_Do%3F
"Seong Ho, played by Lee Jun Ki, lives a poor life with his father, while his sickly mother is hospitalized. But suddenly, he is later on transported back into his father's past and discovers more about his parents and how they met."
(It is findable in net.)
Kimi wa Toki no Kanata e -
http://mydramalist.com/korean-drama/5617/kimi-wa-toki-no-kanata-e
"The story is about 1560 Japan when samurais were trying to battle each other for power and territory and Kimura was dueling with his rival when a time slip sucked them up into 20th Japan and deposited him in Tokyo. ..."
Both are time travel dramas.