I had a similar problem in my last home, which had thick stone walls, and was an unsuitable candidate for running cables.

My solution was to use a homeplug setup, in these data is routed along your existing electrical circuit. Here is an article giving some details about homeplug, unsurprisingly they also sell the gear.

I don't know whether you are in the UK, but am sure that if these guys are not available for you then you will have some local equivalent. Do be sure to get your kit all using the same standard, there are a few.
There are also several manufacturers, and generally people seem to recommend sticking with just one, which sounds sensible. I used Solwise.

I found the technology reasonably straightforward to set up (I too am something of a dinosaur), and definitely an improvement in both reliability and speed over my rather erratic wireless link.