Sorry, I read your question wrong. I thought you were talking about plugging both computers into the modem at the same time.
I had to do what you were doing a few weeks ago when I was in Houston, Texas. I was using a Dell Inspiron notebook, and the ISP was SBC Global with a DSL modem. The notebook didn't have the Yahoo software installed on it. Why? Because you don't need it in the first place. Your computer should connect fine without it.
Anyway, to get the Dell connected, I unplugged the Cat5 cable from the desktop computer, and plugged it into the ethernet port on the notebook. I then reset the modem by unplugging the power cord for 15 seconds. Once the modem was up again, I opened a command prompt and typed ipconfig /release to release the IP address for the adapter then ipconfig /renew to renew the IP address. After that, the notebook was able to connect.