If you're running Vista or Win7 make sure that you have allowed the connection (When you click your character, and click start game, ALT+TAB out of game to see if you get any messages regarding internet access to Grand Fantasia)
If you do not get any messages of any sort, try disabling your firewall (completely) and see if you can login.
Before doing the next few things, i'd recommend trying to redownload the game entirely, just to make sure you dont have any damaged files or anything that leads you in the wrong connection when connecting to the world servers.
If this does not work, disable all anti-virus applications, everything! Still with the firewall disabled, and try again.
If this does not work, try check if your router has some sort of restrictions, and try to fix that. I cannot tell you how, since every router is different from one another.
If you fail at fixing your router or "fixing" it doesnt solve your problem, try go around you router (plug in the internet cable directly to your computer instead of going through a router)
If none of the above helps...... Contact Aeria HERE
and check if your character is temp banned or something weird like that.
If you're not, try contacting your ISP and ask them if they are blocking certain IP's/ports..
Thats really the best advice i can give you