Finally the two computers at home are now networked. With the help of my mom who's taken a computer course as well, we used a 4-port router, 2 straight-through cables, and let XP handle the rest. Windows XP is so convenient!
I noticed something when I checked the IP address of each computer. They had the same IP address! I do not know how that happened, or if it shouldn't really be that way, but so far there are no problems with the internet connection so I guess I should leave that alone.