I guess there's one thing I should explain about these "routers".
Typically, there are two or three components built into the device. A router, switch and a wireless access point (WAP). Each one has a specific function:
The router's main function is allow multiple devices on your home LAN to share the single IP address assigned to you by your service provided. The router will assign each device an IP address, in configured to do so (DHCP) then allow those devices to communicate to the Internet by translating those addresses allowing your ISP to think there is only one device generating all those connections.
The switch is the device that allows the various devices on your LAN to communicate with one another. Most residential routers have 4 user ports on the back, but actually have 5 or 6 ports. The 5th port is internally wired to the router, and the 6th is internally wired to the Wireless Access Point, if applicable.
Wireless Access Point
This device essentially extends the LAN segment into the wireless space, and is not usually dependant on the router to function. One exception is that some routers will allow you to put wireless users into their own separate LANs for additional security, but this is essentially done by blocking the traffic between the WAP port and the external switch ports.
Given this information, even though you manage the entire device from the IP address assigned to the router, the components are independant, and even if you lose the ability to manage the device, the switch and Wireless Access Point will continue to operate as configured.
As that clear? No, didn't think so.
It's not the heat, it's the humility!