Woohoo....it's done !
Opened the lid, removed the broken LCD, got the WIFI antennas out really easy, put them in the new lid reconnected everything, removed the old 512MB memory module, replaced it with a 1GB one and also installed the extra 1 GB module into the memory expansion slot and screwed everything back in place.
Power-up and I get two beeps....o-oh....error message: the memory size has changed ! It is now reporting 2GB of memory instead of the 512 MB it had before...well....DUH....I can save the change....mmm sounds like a good idea

Boots and runs perfectly ! The screen is now looking perfect for the first time in LOTS of years. This used to be my work laptop and pretty soon it started developping vertical lines. First just one but it became more and more. It didn't really "harm" my work but in the end the display was completely dead.
The laptop still worked fine with an external monitor though. But of course that was very clumsy to work with.
A HUGE thank you to Etienne for providing the replacement screen and the extra RAM !

Before this, we actally tried to use a different laptop, a Toshiba Satellite P2100. To our surprise, it simply wouldn't work, even with the XP driver.
The initial communication looked good, and I was able to read a ROM 2 times, but all other tries failed. I tried to run the parallel port in both ECP and bi-directional mode (the only two options in the Toshiba BIOS) but it didn't matter.
On the HP it works fine in both ECP/EPP or normal bi-directional settings.
The really weird thing was that when I tried it with a bootable DOS floppy on the Toshiba, it said on start-up of the EPROM burning software that it could not communicate directly with the parallel port. Our conclusion: the Toshiba Parallel port is not a "true" hard parallel port at all...
Anyway, it works brilliantly now on my old HP under DOS. However I will re-install XP so that I can access internet to verify ROMs and make it possible to swap data more easily (SD cards).