Ah, got that, there's a symbol, three little arcs but with an exclamation mark (!) over it. Hang on, I'll click on that .....
A panel opens up saying 'No Internet, secured." At the bottom of the panel, under the heading of "Network settings" the box labelled WiFi on is blue, the other box next to it labeled Flight mode is grey (and so not active.)
STOP PRESS: nowthisminute another heading has appeared at the top of the panel beneath "No Internet, secured", with another WiFi symbol with only the inner dot bright and the three arcs pale (showing a very weak signal?) saying something like TalkTalk E-7EC** and, bugger me, the bastard's disappeared by now. Seems like the signal is even weaker than a very weak signal. Oh bother. I'll keep an eye on it in case it reappears.
PS, just read your post again, yes; it appears that it is (or is trying to be) connected to my router, the TalkTalk E- etc etc is the Wireless Router Name. Easy for you, I'm sure, but not for dumbo here!
So does it seem to you people that the problem is a weak WiFi signal from my router to the laptop? Well the two are less than a metre apart with nothing at all in between them. Harrumph.
So, where to now?