Thanks all.
Sorry to have pestered y'all with a boring question.
If an i3 over 2ghz with 4gb of ram will genuinely allow me to do different things at once, that's all I need. if I find a cheap, old ( 3) i5 I can go for that.
I don't need lots of gb Hard drive as the main pc and its back up has more than I need. I don't need a sexy graphics set up as I'm not a pixel-changer, nor a gamer.
As Saab says, the old one must have been single core. It required extreme patience.
I'll look at the Morgan re-furbs as they also help keep the price down.
On the Air, SWMBO's ipad 2 has delighted her - except when it died exactly 1 week out of warranty, and Apple wanted UKP 180 for a replacement - that will get limited use for t'net, mail, photos, music and reading.