Who was at fault for starting the Korean War?

The Korean War is an interesting case study in early Cold War policy in that both China and the United States were used by the leaders of North and South Korea in their own political goals.  Korea was divided after WWII into two spheres of influence--the North governed with aid from the Soviet Union and China and the South governed with aid from America and the West.  The leader of North Korea, Kim Il-sung wanted to unite the country under his banner.  The Soviet Union would not help him, as they thought that this would touch off a nuclear WWIII with the West, and Stalin was not ready for that.  Il-sung appealed to China for backing, and North Korea successfully invaded South Korea.  The leader of South Korea, Syngman Rhee said that this was communist aggression and America and the U.N. should help his nation.  After the Communists were beaten back out of South Korea, Rhee wanted to invade North Korea and put the nation under his control.  Ultimately, the war would end in a stalemate; since it was an armistice that ended the conflict and not a peace treaty, technically America and North Korea are still at war today.  

To answer your question in the shortest manner possible, North Korea is responsible for starting the Korean War, but they received aid and encouragement from China, so they are somewhat culpable as well.