Thanks for the quick response and clearing things up. I wasn't the one who set up this old computer for wireless; it was my husband. He just told me there the one piece of very relevant information I had left out of this question to you:
The computer was originally bought 7-8 years ago by and for my husband, and was set up for dial up (and ONLY dial up). So when we got the Netgear wireless router for the house, this computer became the kids computer, and he bought a Netgear USB wireless internet adaptor for them, and that's how it has been connected for the last several years -- this little adaptor has been sitting tucked out of sight behind the computer all that time, and since I really had never used this computer, I had never noticed.
That then, explains the mystery as to why I couldn't get the computer to recognize the wireless router. Now I am downloading the installation software for the adaptor. And I think that will solve the problem.
Thanks again, and sorry I was lacking that very important piece of information.