I'll try to help. I had a problem and solved it myself
Here we go:
1. Always use Internet Explorer
2. Download Active X manually (^What Useless said, Korean stuff will come up. Just wait for it until you get another option to press, or you know it's finished)
3. Check your firewall or Internet Explorer privacy settings. If it is blocking cookies, Infinity and GamenGame won't work properly.
4. You need a GamenGame account, once you get that, just sign in using your e-mail in Infinity.
5. Infinity's server is usually down for people not living in Asia. For me, Infinity opens server at 5:00 p.m. Pacific.
6. Remember this game is still very new and has lots of bugs. Login server might be down a few times so maybe that's why it doesn't work. Just try at different times.
That's all I got, if it still doesn't work, post your problem and I'll try to help.