No, I'm pretty sure that you cannot hook the thing up to a wall jack. Those are phone lines usually, and anything that uses phone lines is dialup. Your computer's internet modem should actually have a cable running to it that looks like a TV cable if it's broadband (I think, I've had comcast and that is cable internet). You will need to ether a) buy a router and plug it into the computer, modem, and your ps2; or

unplug your computer and plug in the ps2 to play. You will probably need cables running around the house, which isn't impossible (they make long cables) but your parents might not appreciate it.
Or you might be able to go wireless, but lets not get into that.