After a bit of work, I’ve managed to get my MacBook up and running. It’s not what you’d call “portable” any more, but it does work. The problem seems to be that keyboard is damaged, and it’s shorting out the powerboard. Because of this, the adaptor won’t power the mainboard or charge the battery.
With the keyboard off, the battery charges OK and the rest of the system seems to be OK. The only other minor problem is that the power button is built into keyboard, which means that the system can’t be powered on, even with the battery charged. The solution seems to be to connect the adaptor and touch the connecting cable from the keyboard to the mainboard, and voilà the system starts.
I’ve ordered a replacement keyboard, so that should sort out the problem, (fingers crossed!). For €70 (including shipping), it’s worth replacing. Now I have a replacement keyboard and a replacement MacBook in transit, so it’s decision time – do I keep the new MacBook and sell my old one, or do I repair the old one and return the new to Apple? Decisions, decisions, decisions.
As a side note, there’s a great guide to disassembling your Mac available from the iFixIt website.