Try switching your default browser in Windows Settings & then try to logging in with browser again. Some browsers have difficulty completing the authentication process.
If you still have issues, then please open Run (Windows+R), then copy/paste this into the prompt:
%USERPROFILE%/AppData\Roaming\Forged Alliance Forever\logs
Click OK. This should open the logs folder that FAF uses. Inside, you should see a client.log file (the Text Document, not the .gz compressed file). Post that client.log file into here so those that can help (not me) have that data to review.