Since Gamasutra posted a pretty lengthy look at the history of consoles in Korea, we're going to give the abridged conclusions here. By all means, check out the full article since it's really quite entertaining. As far as the PSP goes, it's still fairly popular, but mainly used for watching movies while on subways, etc. It's not much of the "short burst" gaming system, which is why the DS has gained a lot of ground there.
The PlayStation 3 has hit a wall in Korea, since most of the "hardcore" crowd have already put their money on the 360. All the negative pre-launch press didn't help, either. The system's still selling, but until the big titles hit, it's not going to have any remarkable sales numbers. The PS3 may, in time, ride on the success of the PS2 in Korea, but until that time, there's nothing fantastic going on. In short, Sony's got to step up to the plate and deliver some good marketing strategies in Korea or else even those Korean console developers will stop trying and that would be a shame, stamping out potential.