Yes. You will need to run setup software when installing your router software specific to Time Warner Cable service. Your PS2 network adapter disc does the setup automatically. Your best bet is to purchase an all-in-one router with a 4-port switch included in such as brands like Linksys, D-Link, 3COM, NETGEAR, Cisco, Orinoco, Asante, Proxim, SMC, or Siemens.
For support information for your PlayStation®2, go to www.us.playstation.com/support. Use the drop-down list to select PlayStation®2 for information specifically on that gaming system.