WFC is the same thing, just abbreviated. Try moving closer to your router if it's having problems with the access point. It may just be that something's interfering with the signal or you're out of range.
Ok, so you went downstairs & talked to the lady in the center. She says 'Welcome to the Pokemon Wi-Fi Club! Would you like to use Nintendo Wi-Fi Connection?'. You select GO TO WI-FI CLUB & it'll proceed to ask you to save your game. Save the game & they'll allow you to enter.
A blue screen should pop up asking you to connect again, select yes, & from there you'll enter the room where I'm at.