1st question: Did you install the router with your computer, if no, do that using the CD.
2nd question: Is a light on the router telling you wireless network is working? If no, troubleshoot the router, if yes, than can you test your router with a laptop that has a wireless card. If the laptop does not work, troubleshoot the router again and also check for your secruity settings which may be blocking access to the network.
If the laptop works, test it by the PS2. If the signal is low, you may need to get a different router that is more powerful, or move your PS2.
Also realize that some apartments have steel frames, so no wirless routers will work unless the router is in the same room as the wireless component.