Checked but that was not the issue, which I summarize her in case others have the same thing: in my case, the config file host name had to be changed.
It defaults to 'localhost', but, for whatever reason, and probably only with my host [pair.com], I needed to enter 'xxx.pair.com', which is where the DB is located.
Now it works perfectly, so I guess I am one of the 1%!
[I have GOT to say that the entire WordPress experience has been astonishing, from the installation [which is so thoughtful you'd think Apple designed it], to the help that is available here, to the templates- everything is just first rate. I hope that, as I gain some experience, I'll be able to give back a little to the community].