Thanks for the suggestions. I've concluded that both the WiFi button and the WiFi LED are in fact not working, likely due to a hardware problem. But since the WiFi itself is working I'm not going to...

There are two buttons on the back of the router, one labeled "WPS/RESET" and the other labeled "WIFI ON/OFF". I am talking about the latter.

Pressing the WiFi button at the rear of the router does nothing - it turns WiFI neither on nor off. The state can be changed only via a browser. On the other hand, the WiFI LED at the front of the...