Do you know what a USB connection looks like? Is your adsl modem connecting via USB to the PC, if it is then you cannot just use this socket.
However if the adsl modem is connecting via a network port then yes you can. I think the cable that came with the DG834G box is an ethernet cable and will only fit a network port, so if this cable that was in the box fits, then yes you already have a network port and won't need an FA311. The DG834G has a built in adsl modem so you won't need your old modem.