Here. A VERY VERY crude drawing I did in about 2 minutes with paint. Your stuff doesn't have to look exactly like this. This is a 'scaled down' model. Your computer may be downstairs, PS2 upstairs, and routers in your backyard for all I care. This just shows you how to connect the things. The red is the ethernet cord, and the green is the signal from the router to the computer. After you set it all up, you may need to make a new internet setting for your PS2.
Just to be on the safe side, try at your own risk. I doubt anything will happen, but I can't garuntee it.
Hope this helped.