If a website is located to be unavailable, the Pi goes into “deep probe” way to find out the area of the outage, and lights up so. In case the light is green, the link’s not dirty; best go to bed if it lights up red. As a bonus, logs are maintained of all deep probes, which might prove useful for diagnosing ISP problems.

A screen in this way could go a ways toward ensuring you will reduce the workload for you as de facto IT support, and keep plugged in. Of course for a bit more info regarding the connection speed with retro styling, you may need to throw a Dekatron at the occupation.