Hi andsheph4 and welcome.
These are analogue inputs designed to import analogue audio/video to the Vaio's hard disc for editing and burning to disc using video editing software.
As far as I know, you cannot stream video in full-screen using Windows Media Center as this is based on digital video. This used to be possible using 'Vaio Zone' and tuning the analogue TV tuner to the AV inputs.
However, even if you could set this up, this is unsatisfactory for gameplay because of the latency in the analogue TV Tuner.
Silly question - but why don't you simply connect the PS2 to the monitor direct?
