The indicator lights for active Ethernet connections might help you troubleshoot problems with a Wi-Fi router. While Wi-Fi and Ethernet may seem like two utterly different pieces of technology, they combine in a wireless router, in which the device’s software interconnects networking traffic across the two types—and on some models, across a third via DSL or cable standards.
That can provide a problem if the Wi-Fi part of the gateway remains active and healthy, meaning that client devices, like smartphones and laptops, can connect to the network and report back that everything’s fine, but the Internet connection appears dead.
I’ve found frequently that when a Wi-Fi router appears at fault, Ethernet is the actual culprit. While Ethernet is an extremely reliable and long-running technology, cables fail through wear (if you move them around) and over time. It’s especially a difficult issue when Ethernet is threaded through the walls of your home. (Some homes were also wired long enough ago that they use an older standard of Ethernet cable that can’t consistently support gigabit Ethernet signalling.)