I tried this. I had a wireless connection from my main cmputer downstairs to mine upstairs then linked that computer to my slim PS2 and it didnt work. I always thought it made sense that it should work and mine might have been a special case but that mutha wouldnt work for anything!!!
I just went out and got a wireless adapter from radio shack for $99. Keep in mine though that I have the slim PS2 if you dont and maybe it works differently to the fatty.
