your in luck, i just installed that exact adaptor so I could play madden 2005 on my ps2. You need a wireless router for that adapter to work, but you said you have it so that is no problem. You need to have the PS2 adapter as well as the Linksys Game Adapter.
This needs to be screwed into the back of your PS2 like the picture - http://www.us.playstation.com/periphera ... SCPH-10281
If you do have the PS2 adapter already and it still didn't work, you might have forgotten to put in the CD for the Game Adapter. You need to follow the directions on the CD for your Linksys Game Adapter to work.
*Dont worry about what kind of router you have, it doesn't matter as long as its wireless.