Ah, a Conflict of Laws question. This is considered one of the most, if not the most, difficult areas of law- what to do when one set of laws says one thing and one says another. I'll venture an answer, but these conclusions are only tentative.
It's a bit difficult even to get started because some conditions of the hypothetical aren't very realistic. When you say that the government of Defiancia orders its courts not to hear the case, do you mean the Grand Negus of Defianca says to the Chief Judge of the Super-Supreme Court of Defiancia, "No court of this nation shall hear this case?" Or do you mean that the court hearing the matter rejects the suit on procedural grounds (i.e., NCSoft failed to follow the Defiancian courts' rules of procedure)?
In either case, given that the country seems to have a known history of allowing private servers, NCSoft is unlikely to bring its suit there. Instead, it will file suit in Korea, or the United States, or the U.K., or any number of other places where potential consumers of its IP are located and not paying it. Basically, anywhere NCSoft is suffering damages. NCSoft can probably obtain a judgment in its favor in such a court.
That is only half its battle, though. Now, NCSoft needs to get its judgment enforced. If the servers were in the U.S., it could just take the judgment to a sheriff's office and have the sheriff seize the servers. Even if the judgment were from, say, Korea, and the servers were in, say, the U.S., it could do something like this, using various international law devices that have been around for centuries. Essentially, most countries agree to enforce each other's legal judgments, whether by comity (i.e., international niceness), treaty, or special request.
But we've established that Defiancia refuses to shut down servers, for whatever reason. Thus, it won't act out of comity with the foreign judgment, and we can assume there aren't any treaties. Still, NCSoft's attorney might file a new action in the Defiancian courts to enforce its judgment. Or the attorney might submit any of several kinds of international requests for assistance to the Defiancian government.
If all of those fail, NCSoft would likely move out of the lawyer-arena entirely and complain to diplomats (presumably South Korean rather than American, but one never knows). Those diplomats might complain informally to the diplomats of Defiancia. If you're asking if South Korea will go to war with Defiancia over this, it seems wildly unlikely.
All this becomes much more questionable if Defiancia is not an actual nation at all, but something like an oil rig someone has claimed as a country. In that case, any of the several courts involved are likely to determine that "Defiancia" is really part of, say, Great Britain, or the U.S., or whatever country is nearest. To my knowledge, no one has legally tested the notion of sovereign oil rigs and the like. I find it hard to believe countries would allow possible tax revenue to slip through their fingers that easily. Now, NCSoft may still have trouble getting its judgment enforced if Defiancia is out in the middle of the North Sea, but if it's recognized as part of a country or otherwise subject to a nation's jurisdiction, it can eventually get someone to do it.
As with so many other things I've seen proposed here and elsewhere, this is something that looks like a quick, easy solution and isn't.
Again, as always, the foregoing should not be taken as legal advice.
