Games & gear: Playstation 2 Network Adapters

Playstation 2 Network Adapters

A few months ago I used to play Playstation 2 games online using the PS2 Network adapter, I connected it to my Telewest supplied WebSTAR modem through the Ethernet port. Of course I couldn't use the Internet Connection on the PC at the same time.
But now my Playstation 2 is upstairs along with a second Telewest Set Top box. I noticed at the back of the box that there is an Ethernet port here. I am just wondering if I can connect my PS2 to that port and play games that way. I use the second set top box to watch TV in my bedroom, I tried it today and the lights at the back of the Network Adapter did flash and work as normal... Just as if it was connected to the modem, but I cannot play any games and attempt to connect to Central Station etc. as I have misplaced my memory card.

Thanks in advance...