At this point there seems to be no rhyme or reason to anything it's doing.

After a reboot of the machine, Firefox is suddenly OK with any site.
Which I'm not complaining about. The network card seems to play
nicely when it feels like, but when it doesn't no amount of twiddling,
rebooting or killing power seems to make a difference. It works when
it feels like working. The wireless card seems to work 100%.

The network card is a Realtek. Not sure about the wireless.
(Whatever HP decided to throw in there. It's a Pavillion, not a lap
top. So I've also checked that the card is securely seated. (Though
Vista, for all it's other faults, has no prolem with it.)

Yesterday, Firefox refused to launch until I did a full reset. Not
sure why. I'd click on the icon, it would do the little flash like
it's launching thing, and then nothing would ever happen. Tried
several times over several desktops.