No internet after removing Norton

On my desktop I found that it was running very slowly and Norton internet security could not up date. I followed Norton instructions and dumped the icon in the trash then downloaded and executed the uninstall app which used a terminal screen. I followed all their instructions and rebooted the computer. However when I try to open Safari it says I am not connected to the internet. The status bar on the top of the screen indicates that I am connected. When I check network preferences it says that I am connected to my Wi-Fi network but there is also a second listing for Norton Security which it says it is trying to open. More reboots and second running of the uninstall app does not help.