Believe it or not this was my fault - I think. It was a matter of permissions
I have 2 instances of XP on the machine that has the printer attached; was having problems with the first one (XP1) so was using XP2 - the test one - as the default. Only thing was the laptop, upgraded from vista to W7, wouldn't print since the upgrade -
had all the messages like Offline, Access Denied and so on, sometimes didn't even show up in the Printers screen. All cables fine, printed from XP and no trouble.
I tried all suggestions (on the W7 m/c) - no joy. Finally as a last resort looked at the XP machine, and found that the printer was marked "Do not Share". So I shared it, and Bingo!!! now it is going just fine. Do I ever feel an idiot!
Piecing it together: I upgraded the laptop at about the same time as the trouble with XP1. The problem with XP1 was that in the course of downloading SiSoft Sandra, Windows - so perhaps it was its fault after all :-) - downloaded a whole lot of junk, to
do with ActiveX and .NET, about which I know nothing, and completely filled my C: partition - couldn't do a restore point or anything.
So I started to get rid of everything I could from C: including the printer software and, as I realised, the drivers. When I had some space. I re-installed the drivers, printer working fine locally, but I forgot about sharing it - must be the default - and
that's why it had ceased to print.
(Checking XP2, it also wasn't shared, but probably had never been configured as it was only a test partition.)
So that's my silly story, and it may help someone.
As this thread is getting so long, I am going to do as Debbie suggests and start a new one,
with a shortened version of this post, and will mark it solved - on my own thread of course. I will add a link to this one if I can find out how.