iMac Won't Auto Connect To Internet Via Ethernet Cable

I'm Using An iMac OSX Leopard, And When I Turn On My Computer The Internet Isn't Connected Even Though It Works. I Get Server Not Found In Safari And Firefox. I Have To Unplug The Ethernet Cable And Plug It Back In For It To Work, But If I Turn Off The Computer When I Turn It Back On It Doesn't Work Again. When I Open Diagnosis Everything Is Connect Except For Internet And Server Until I Unplug The Ethernet Cable And Plug It Back In. I Tried Using WiFi But The Same Thing Happens; The Internet Works, But It Doesn't Auto Connect Even Though The Computer Is Set To Remember The Network And Connect Automatically. There Is No Firewall On. Are There Any Solutions? Thanks For Your Help.