Fortunately, I have been able to bring my computer back to life. The display consists of two parts, the TFT display itself, and an electroluminescent panel behind that to provide illumination to the screen. I could dimly see that the display was OK, although without the backlight it wasn’t usable, so it had to be the EL panel. This is supplied by a high-voltage inverter circuit in the top (display) half of the case. What had happened was that one of the wires to the inverter had snapped near the hinge. It’s not surprising, given the number of times that the case gets opened and closed; the hinge is definitely the weak point of the clamshell design.
All I had to do was to solder the two ends of the wire back together and tape over the join. It was relatively easy to diagnose and repair. My computer is even more of a Frankenstein-like creature than ever, but it’s alive!
So it looks like I get to keep my reputation for being able to fix stuff, but more importantly, I have a working computer again. That’s really useful, because I’m moving to my new flat tomorrow. I’m looking forward to that.