You have a few options.
A. If you have a new LCD monitor, it may have YCrCb component inputs, or Svideo, composite.
B. If you have an All in Wonder, or standard video capture card, plug in through that (usually just svideo or composite unless youre rich).
C. Some DV Cameras have video passthrough. Connect the PS2 to the AV in, and DV to the firewire ports on your PC.
D. Get a VGA Box, which many are unreliable and only available in Hong Kong.
As far as I know, BNC will only work with composite (if you have one BNC connector only). The PS2 outputs over component in two methods, YCrCb (YUV) or RGB (which doesnt stand for red green blue, in this case it is referring to the European SCART connection) I tried component to my old monitors BNC "RGB" connectors and it did not work in either mode.