I have a new windows 7 computer and an old windows Me internet to older computer.

Use what they call an Ethernet cable, from an output jack on your router to the Ethernet jack on the ME computer. If there is no etherrnet jack, you will need either a plug-in board with such a jack on it, or you could go wireless with what is known as a dongle (a USB-connected wireless receiver / transmitter). If you use a dongle, you will have to load software to run the USB device.