Frankly, I'll sum up the situation in here.
There is something called the Aegis system which blocks missiles. I think they could also block nukes, and our country has tem. Anyway, the nukes may or may not prove to be a problem, because there are anti-missile systems in our country, but no one's sure if they can block a nuke
Also, our army is 0.5 million strong. Our reserve forces are outstanding, the second largest in the world. Our country's army is highly advanced with K-2 tanks which match the American Abrams, the K-9 self-propelled howitzers, and such. The Daewoo 11s are now expected to come out.
Our navy is modest at best. It's a small navy, and with North Korean submarines, we can be beaten if we don't work in defending against irregular forces, in which the North specialize in.
Our air force is acceptable. Although it is modern and advanced, it is small in numbers, yet the North has mostly obsolete models, so we can survive.
Overall, we would win. Note that I assumed that no other country will intervene, which is highly unlikely