It seems that Korean users, or anyone who simply want to use the Korean Playstation Store in the near future will be unable.
This decision has been made by Sony, out of no where if we may add, to comply with a new act that is planning to go into effect in South Korea in less than two weeks. The reason for the suspension of the Store is due to the fact that it asks for real name or age verification if the PSN account is under 18, which will soon be illegal in Korea.
Due to the fact that Sony can not change this before the law goes into effect on the first of July, they will be taking the Playstation Store down indefinitely. Portable devices that use the Playstation Store such as the PS Vita or PSP will apparently not be affected by this whole fiasco.