Hooking up PS2 and PS3 to LAN

Ok, this may be a dumb question, but I'm not above asking one. Anyways, we have our comp. hooked up to a wireless lan connection. I also have a PS2, and later this year, plan on getting a PS3. Our provider says for an additional connection, it would cost another 10 dollars a month. I don't really care if my comp and PS2 are both being used at the same time. I mostly want to be able to update a PS3 and that would be about it. I thought I could get a regular ethernet cable and unplug the comp. from the modem and just plug in the new cable to my PS2. When I sat it up for an automatic search, it says it can't find a connection. I hooked up the same cable to the comp. and it worked fine. So then I went to the advanced settings and there were some things I'm unsure of. I can find our IP address, netmask, primary and secondary DNS on our comp. I'm unsure of the default router and what kind of base and duplex we have. I was just wondering how I could find them out, and if I'm just wasting my time, and need to pay the extra 10 bucks a month. I've read on other sites that Sony doesn't recommend using a router. So I'm not too sure of what I should do. Any suggestions?