It is theoretically possible to create an unhackable system. From Instapundit today Neil deGrasse Tyson shows how not to talk about the subject.
The problem fundamentally is that implementing an unhackable Internet to eliminate the North Korean hacking threat would destroy the Internet as we know it today as well as most business productivity programs as well as most other software running today. The economic loss would likely eclipse the entire IP industry's economic output over many years. In short, it's not worth doing this today and likely won't be worth doing for decades. We need better defenses against hacking a lot quicker than that.
For those interested in the people actually working to fix these problems, take a look at LANGSEC.