Thanks all. At the risk of hacking off people who wonder why I didn't cut to the chase, I ended up transferring the screen to an old carcass I had hanging around, along with the HD and RAM, and whaddya know, it's all fine.
Funny thing tho'... after I'd installed the screen then started t'other one, it took an absolute age to boot up - just sat there with the HP invent screen doing nowt for about five mins, to the point where I'd pretty much decided the CMOS in that one must have gone too (we're talking decade-old pooters here, after all). Then it suddenly went into Windows, and seemed to be behaving normally. So I ran some diagnostics/tuning stuff, defragmented, then restarted. It restarted almost as normal, but came up with a 'scheduled disk check' message. I let it run, and it found & fixed shedloads of issues, then restarted again, and now it all seems to be tickety-boo. The 'shedloads of issues' making me think it probably was simply software that had got its knickers into a twist during that aborted HP softpaq update.
Anyway, like I say, it all seems to be up & running again now, and me eldest's very pleased, so al is vell.