Whenever I try to access the Internet, I get prompts from the small computer icons in the notification area which switch from "local area network connected" to "a network cable is unplugged". This prevents me from using the Internet because the pages that I want to access don't show up. When I try to access Messenger, I have to troubleshoot and the system tells me that the default gateway is offline. How to I fix these issues.

This could be caused by TCP/IP stack problems, a bad cable, or a bad interface. I would try a different network cable first if you have another (working) one handy. If that fixes the issue, you're done. If it doesn't fix it, then you might want to try uninstalling, then reinstalling the TCP/IP stack. If that doesn't fix it, you need to test to see if the interface (NIC) on your computer is broken.