If N/Korea does start conflict (It would wait for S/Korea to retaliate, either by sinking a N/Korean ship which would pass into its waters after N/Korea has now scrapped the agreement that would prevent 'accidental' clashes, then claim the act was intentionally aggressive), then the USA would no doubt intervene to protect its ally. This should force the intervention of the UK & possibly other NATO forces along with UN peace keeping forces (We are still talking about a military force numbering over 1.2 million, no matter how malnourished or poorly trained). Targets in N/Korea will be strategically bombed in a campaign to take down what infrastructure is present, and ground forces would be sent and used to repel N/Korean forces, not attack them.
I don't know whether China would be pressured into also invading from the north, or would the NATO forces want to take N/Korea for themselves. Think of it this way, if the US of A takes North Korea, and keeps a substantial force to the South of China, then you have an immediate deterrent for future aggression in the future between those two nations and their respective allies. If China is railed into help however, they gain further land and the US has less claim to N/Korea.
Either way N/Korea would be defeated, if they tried to use any sort of nuclear device then they would gain international response and be fucked over sideways, they could be used as an example case to other nations (Iran or Middle Eastern countries) that using nuclear arms would have incredible consequences from the international community.