Not sure what your problem could be without more information, however, I can offer some suggestions as a rule of thumb solution. I know some suggestions may sound basic and superficial but in a lot of cases it works.
For PC Issues
1. Make sure that you have the latest version of WGT installed. As of December 31, WGT golf does NOT support Flash. If you have a Flash version installed, it will not login. You need the newer WGT Launcher program.
2. Clear out your cache and history files. Some older files are in conflict with the newer software. When it tries to access them it fails.
For Apple Mac, I hear that there are many people having issues loading WGT. I do not know the Mac solution since I play on a PC.
I hope this helps. I am not tech support. I am just another player who had similar issues.