You have a few options.
1. Get a dedicated VGA box for the PS2.
Pros:
-Easy to do, no drivers to mess around with, no need to open your PC.
-Relatively inexpensive
Cons:
-This has the drawback of having to unplug it when you are done with PS2 and want to get back on the PC.
- Likely wont work with PC sound. You'll need to buy a seperate adapter and connect it to the 'line in' of your sound card.
2. As the previous poster suggested, get a TV tuner or AIW type card that accepts input connections.
-Pros:
-No need to disconnect your PS2 from PC after you are done gaming.
-Can easily record and edit movies of your gaming session(s) if desired
-Audio works right through your PC audio setup
-Cons:
-can be costly (if you choose the AIW route).
-relatively difficult install. installation requires opening up your PC and quite a bit of drivers/software to install.
Hmm, out of these I personally perfer #2. I am not saying these are the only 2 ways to do it, but these are probably the most common ways this type of thing is accomplished. If you currently have a card with Vivo you can also basically use this along with the same audio adapter you need in setup #1.