For those who are facing the same problem in trying to book and pay for a domestic flight with Jeju Air but unable to do it, these are the steps you can follow through.
(I have tried 6 days of numerous heartbreaking and frustrating attempts. Maybe I am abit too dense and slow. In the end, I have found a straightforeward solution. )
1. Goto http://www.jejuair.net/ to search for the Flight No., Timing and the destination.
2. Then send an email : firstname.lastname@example.org on the Flight No., Timing and the destination.This is to ask them help you do the bookings.
3. Now it is time for you to wait. Jejuair will send you a reply with a reservation number.
4. Reply the email on your mode of payment and the numbers in your card. If not just call them at +82 1599 1500
5. If you should call them, you will get an immediate confirmation. By email, you will have to wait for their reply about your confirmation.
Hope this is helpful for those who have give their heart and soul in trying to make the many many failed attempts to do the booking.