It seems it won't connect to the router at all. It says that it cannot get an ip address and that the default gateway does not exist. I would suspect the dhcp service isn't working, restarting the service then plugging in the LAN cable gets a home network to show up with Internet access, but it's just saying that. It doesn't have Internet access or connectivity to the router (cannot ping gateway). It later reflects that in the network and sharing center.
Ps. The router is brand new and working fine. I have tested it with numerous devices on all ports.