Hi,
Please confirm .... is this the back of your new Video Card ?
http://rog.asus.com/wp-content/uploads/2012/11/ASUS-GTX-680-4GB-DCII-display-799x347.jpg
If so .... the connections shown are female ( no pins )
Your adapter would need to be a male DVI (pins) to VGA adapter.
See here: click here
The first adapter you linked to is a female DVI - you must get the correct one.
The Belkin is the correct connection.