Network Time-Out

I have 2 computers networked to a third that is used for the modem connection. Using Win 98 SE and Linksys.When you connect to internet through the one computer it dials up and goes to the home page.Great ! The other computer,when dialing on to internet “times out” and you have to hit reload to bring up the home page.It does make the connection to the net but not fast enough. Any Ideas ?