So, let me see if I am understanding you correctly. You are looking to take your wireless signal from an access point, and then make your old computer in to another access point, for some of your wired computers?
You will probably want to use some version of linux. Here is a walk through for how to do it with SUSE 10.0, to create a router from an older computer. I am sure that there are some other distros that you can you.
The only issue that I would think that you might have is taking the wireless signal and transferring it to the wired cards. But google it and I am sure that there is an answer for the as well.
Cheers, and good luck! This should make a great DIY project!