How to hook up to modem wirelessly with ME?

Hello! I am pulling my hair out trying to find a way to hook up a 2nd computer to my dsl modem. I have a compaq series 5002US that has windows ME on it. I'm wanting to get it connected to my siemens gigaset se567? Please if anyone can point me in the right direction to get help get that accomplished, it would be greatly appreciated.

If there is a way to do it I would really like to keep it as ME cause I have the factory restoration cd and if any problems I know how to reinstall windows. If I have to upgrade to a new windows on that computer I am not sure what I would have to do even?? Or if it can be done with this specific computer. Thanks for any help that you all can offer.