In a strictly conventional war, I think they would suffer a defeat of Gulf War proportions. They are a teetering regime, ruling over a starving populace, with outdated soviet era hardware.
Of course the trump card (as it always is) is nukes, which we believe they have.
36,000 soldiers stand guard to a weak Republic. Believe what you want.
I sense that if the US is involved in a conflict, the strategy may be to kill the entire leadership and destory several key military areas of the country. I'm sure we have intelligence regarding where nuclear weapons and some bio-weapons are stored.
There also has to be constant dialogue with China now stating that if they can't reign-in NK, China stands to lose a great deal economically. Money talks, bullXXXX walks.