The world is trying to force regime change through crippling the country with economic sanctions.
After the examples of Bosnia, Kosovo, Croatia and other Western interventions designed at producing regimes favorable to capitalist exploitation, the DPRK has been on the defensive.
Western commie-toppling hit a brick wall in China, but the Chinese are already capitalist, so Western governments don't say anything bad about their government. Once it became clear the Chinese government wouldn't be toppled, the West just shrugged. The word "Sino" is a good acronym as well: "socialist in name only."
But the DPRK isn't capitalized, so to avoid going the way of Eastern Europe, Ukraine, or Serbia, they built their own brick wall: the plutonium bomb.
They're not pushing for nuclear war. Anyone who believes they really want a nuke war is falling for sensationalist media spin. If you were alive during the Cold War, you know that even if you don't intend to use your nukes, you still have to brandish them. It's a diplomatic method for achieving goals.
Right now, the standoff is like this: the US still wants to change the DPRK regime but won't say so. The DPRK is demanding that the idea of regime change end, along with the crippling sanctions. This demand is in the form of the bomb. Even though their heavy artillery is far more powerful than their bombs, the bomb is the polical counterbalance to the idea of regime change.
Why does it drag on so long? The DPRK intentionally pretends it's going to give up its bomb in exchange for this concession or that concession. That's because the US demand of nuclear disarmament is unacceptable to them, not to mention hypocritical coming from a nuclear-armed state. Because the goal of regime change goes unmentioned in the negotiations, but it's the real US demand and the North Koreans know it. Essentially giving up nukes = regime change. It's not gonna happen. The North will jerk the US around until the US gets tired of it and revises its demands. Then the North might make substantial concessions.
The DPRK government, whether you like them or not, wants to survive, and they're going to. Now that they're nuclear-armed, in fact, the US can't afford for them NOT to survive. If it falls, its nukes will be in the hands of an unknown and could go anywhere.
Kennedy managed to resolve the Cuban Missile Crisis (which his foolish hubris was responsible for provoking) by taking Cuban regime change off the table. That might work for the DPRK, but until then, the US will still try to strangle the North with sanctions, while the North will keep holding on to its bomb.
The North isn't going to just go ahead and use its bomb, unless they are starved into such desperation that their government will fall anyway.