From doing a bit more reading, people are saying their iBooks won't boot at all if the GPU is loose. In my case, it does boot (I can hear the hard disk rattling away as it boots into OS9), so do I have a loose GPU or is it the inverter cable? Applying pressure to the left of the trackpad (another commonly-mentioned GPU fix) makes no difference.

I know it's booting into OS9 fine because if I leave it for a minute after the hard disk activity has stopped and then hit the power button, followed by enter, it shuts down.

I'll need to borrow some tools to open this up, but I'd rather leave the GPU alone if it isn't the problem. If wiggling the cable produces something on-screen, I could try swapping it out with the one in the 500 to see if that fixes it. Then just look for a replacement cable.