The Playstation 2 connects to your television using a “Composite" Signal. The cable has three connectors, yellow, white and red. One jack sends the audio (left), the second the stereo (right), and the third the video, respectively.
This signal cannot be connected directly to a PC monitor. You require an adapter that costs about £40 - £50. I have added links to two examples of these. They allow you to connect your PC to them as well as the games console so there will be no need to swap cables.