<<< It says LAN connection 6 has limited or no connectivity >>>
How many network adapters (Local Area Connections) are there? If you have only one and it numbered as "6", it would appear that Windows has been reinstalling the network adapter over and over again. Create a System Restore point, then go into Device Manager, uninstall the network adapter, reboot and let Windows "find new hardware" and install it. Then see if it gets its correct IP address from the router.