Also, it's 35 miles from the DMZ to the center of Seoul, but Seoul is a big city. There are parts of Seoul proper less than 25 miles from the DMZ, and the metropolitan area extends much closer still. Hundreds of thousands of people in South Korea live within comfortable artillery range of North Korea.
And, contrary to some popular theories, actually attacking your neighbor is not that useful for bargaining. All it does is to make other countries very angry and call for more hardline policies. So the best NK can do is keep its madman shtick, not actually use the missiles, and demand larger concessions. But other countries would want, in turn, some semblance of promise that NK will stop being so crazy if it gets economic aid. So we're back to stalemate.
NK rulers aren't idiots, they have access to the West (media and travel) and they know about the relative military strength and probably aren't to keen to have Democracy™ being forcefully implemented on them.