Better of getting a router and register the mac address of the router with your service provider. Thats what I currently doing. Im using a Netgear RP614 and its quite easy to set up and never had much problems, I believe its far easier then messing around with network sharing. When you load up the Network Access Disk thats comes with the ps2 network adaptor you'll need to configure your settings through that.
As for connecting it through your PC yes it is possible but I personally havent used this method but can briefly describe how it can be done. 1.) Power done the computer, playstation, etc. 2.) Ensure one of the netwrok cables is connected from the cable/adsl modem to your computer. 3.) The crossover cable is then connected from your ps2 to a spare network port on your computer. 4.) Make sure your computer still can access the net. 5.) Run through the internet sharing wizard so that the ps2 can share the network connection, depending on your Operating System can be slightly different. 6.) Finally using the network access disk that comes with the playstation 2 network adaptor run though the settings. The wizard is quite good with this.
The router is the best option. My son connects his X Box into my router, a RP614, and it worked straight away. You will not need to register the address of it as the router hides all the pc's/ consoles.
The other advantage of a router is you can connect other pc's easily and they are protected by a hardware firewall.
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