Well, I've been trying to make sense of that site following the url you provided, and I' afraid I can't even get as far as you seem to have done, because I haven't reached the page where the requirements you refer to are specified.
I got past the first hurdle, but alas no furher. As usual with Korean sites, you have to first get a code from the site sent either to your email address or your cellphone number before you can start the entry application proper. I tried the cellphone method first, but I never got a text message with the required code. Maybe it doesn't recognize non-Korean cellphone numbers (though other sites I've used do). In fact if you click the l link in "English" labelled MembersForeign, you get a pop-up in Korean only (!!)) telling you you have to use the email verification method. So I then did use the email option, and that apparently worked. I got the one-time code in my inbox within a few seconds, cut and pasted it from there into the web form and got the message on that form saying
본인확인 메일인증이 성공했습니다. 확인버튼을 누르시고 다음을 진행하세요
which means "Your email authentication check succeeded. Click on the OK button to proceed to the next stage." So I clicked on the OK button, whereupon the window closed and... zilch. I guess a further page is meant to open where you fill in the ID particulars, but it didn't for me. Maybe it's because I was using Chrome, where many Korean sites work properly only with (preferably outdated versions of) IE.
So I fired up IE, but now catch 22 set in. I tried to start the process again, but when I typed in my email, I got a message saying this email has already been verified as belonging to another user, and I wasn't allowed any further . GRRRR!!!
So I never even got to see the page that's challenging you...
I did poke around in the public areas to see see if I could glean any
info regarding your various questions. In their "payment info" section they do claim to accept credit
cards and don't specifically say "Issued by a Korean Bank only" as some
sites do, but you have to type in a valid card number so it can be
validated before the rest of the form then redraws with fields specific
to your country and credit card provider. This is a very common Korean
trick, but it means you don't get to know whether they accept your
particular type of card until you've given them your full number, and
once again there's nothing useful I could do, since obviously I can't
input your card number to see what happens.
What might just be of some use to you is the in-site email form. Just below the login/join section on the left hand side of the customer service page, there's a link labelled 이메일 문위 Click that, and a form opens up through which you can send a message to the site admins from the web page itself. Or you may be able to get it directly usinghttp://www.upiece.co.kr/member/mailto_webmaster.asp?kind=undefined
The fields on the form are as follows:
The drop-down item near the top is "Type of message" and can be left at its default value, which means "Contact main site admins". The field below that is for your email address for a reply (look again for 이메일주소
in the label of the field to make sure you're putting your address in the right place). Then the field below that is Topic, and then you type your email message in the large box below then click the big orange button right at the bottom to send it. If you keep your message in simple English it might get across.
Although my reading and listening abilities in Korean are pretty good, I am not at all skilled at writing the language, and I'm absolutely lousy at speaking it, thanks to my lack of speaking and writing practice (not to mention not having started to learn it until I was close on 60). So I don't think it would help much if I tried to deploy my dyslexic-infant-level written Korean on your behalf,
As a bit of background, I suspect the reason why you've lost your login facility is a major crackdown in the middle of last year, when the government compelled all sites to collect additional ID evidence from their existing users and also to expire all their passwords and force them to create new ones within a limited period (30 days ISTR). I managed to do this for all the sites I'd subscribe to apart from MBC, which refused to renew my membership without stating a reason. As for ID evidence, without having reached the crucial page in question I don't know what this outfit requires. Some sites require you to upload a photo of your main passport page, drivers' license, or social security card. You put the image on your PC, then click a button on the web page and navigate to the location of the graphic file, then click another button to upload it to the Korean site. You then have to wait several days before you can log in. I never provide my passport details, but I have indeed used my driver's license on several sites, including some that didn't name a driver's license as an acceptable item, and until the MBC incident, it's always been accepted. I even got away with uploading a photo of my senior citizen's bus pass (!!) on one occasion, and my university alumni membership card on another. I doubt whether they really check these things all that carefully, and if it has a photo, some sort of offical looking crest and your name tallies, I suspect they just accept it, unless your from some "rogue state" or other.
I really wish I could be of more help, but maybe this will get you a little bit further along the way. Let me know if you think I might be able to help any further.