No..assuming you have cable. In some instances Verizon will give you a dsl modem/router, but in your case I will assume you are using a cable modem.

1) You need a router (wired or wireless, both are about the same price now)

2) network adapter for your ps2 if it's not already equiped with one.

When you get a router ditch that USB connection and use an ethernet cable and plug the computer and ps2 into the router.