Getting a "Limited or No Connectivity" indication means that the network adapter has failed to get its IP address from a DHCP server (the Router) and Windows has defaulted to allocating a "169.254" APIPA address (Automatic Private IP Addressing). This won't let you connect to the router or the internet, although file sharing over a LAN is possible with APIPA addresses.
Go into the router's settings and check that its DHCP server is enabled. To do this, connect to it by ethernet cable, give your network adapter a fixed address in the same subnet as the router (e.g. 192.168.1.2 with Subnet Mask 255.255.255.0) and then type the routers IP address of 192.168.1.1 into your web browser.
[To revert to automatic IP addressing, set *BOTH* the IP and DNS sections back to getting their addresses automatically.]