I am a realist here. Lets ask ourselves some questions.

First, is North Korea worth damaging one's diplomatic relations with strategic trading partners in North America and Europe?

I do not believe so. Russia may be a big trading partner, but Russia is not everything and everybody.

Second, is China's military as ready and experienced as the South Korean military or the US military? The South Koreans have been in a cold war with North Korea since the 1950s. They know their geography, the choke points, and kill points of the land through and through. Same goes for North Korea.

As for the USA lets see: Korea, Vietnam, Iraq x2, the Balkans, and Afghanistan. No other county has the sheer amount of experience in modern, urban warfare as the United States of America. Also, drones anyone? 

 What military experience does the Chinese military have besides marching in parades and bullying some Tibetan monks who would sooner set themselves on fire than pick up a gun, much less a bo staff? 

Third, can China afford to militarily intervene in a war in the Korean peninsula?

 Sure, just like Iran could afford sending expertise and weapons into Iraq. Whether they have the balls to send troops wearing Chinese fatigues is the question. Then again, one can tell a Chinese from a Koreanv very easily, while the difference between an Iranian and Iraqi is not as clear cut. If China did send troops not in uniform, they would be killed and exposed.

Honestly, I don't think China would risk much if the Koreans went at it. If they backed North Korea full on, then they could kiss Europe and North America as a market good bye. Good luck supporting a 8 to 10% growth and a growing middle class by selling to Russia and a bunch of third world nations.

Actually the Chinese will have their own drones really soon now.  That governmental hacking unit is really paying off.

http://www.dailymail.co.uk/news/article-2011533/China-building-army-unmanned-military-drones-rival-U-S.html

Well you see the Chinese are investing in infrastructure and economic growth and when it becomes more stable and when it becomes as economically powerful as America, they will focus a lot more on their military.

China has better relationships with South Korea not only in term of diplomacy but also including the population who mostly dislike North Koreans and like/love South Koreans.

You guys apparently seem to think China would be fine with the US having military presence at its border literally. China would never let that happen which is why they wouldn't back off the Korean conflict so easily.

This is the reason I believe America should stop having bases in South Korea. If the US agrees to let go of its bases, then I believe the conflict would sort itself out with South Korea winning the war. However, note that it's not good either for South Korea to win the war, since they are so much more advanced than north koreans.

all your base are belong to us

China only needs to conscript 1% of it's population and the world is fucked.

4. Add the most important reason: business. Even if NK buys weapons, other tech and goods and food from China, it's a country on the brink of economic catastrophe and a market far less important than SK and any other reasonably sized developed country.

If China militarily intervenes, it would be to help South Korea/US/whoever else topple the North as quickly and efficiently as possible.

A protracted conflict between the Koreas would mean a flood of North Korean refugees entering China. China does not want this at all. I remember there being rumors (from wikileaks maybe?) that China wouldn't mind a unified Korea under the control of the South, where they have some exclusive rights to natural resources in the North in exchange for no US bases north of the current DMZ. That throws a little bone to US while keeping us from building bases on their border, the South Koreans can pay to educate/modernize/feed the North, and they get access to cheap labor and natural resources.

I think it all depends. If N. Korea start the fight, then China won't risk confrontation. If the USA starts it, then China will assume that it is a precursor to an invasion of China, and will defend themselves and their ally.