Lido from the post below seems to have solved the problem. I'd never heard of it, though I think I may have used Hard Disk Toolkit once long ago.
The logic board is freshly recapped. It was my first successful attempt at it and I'm rather proud of myself for it. The screen is bright and crisp and the case is only very slightly yellowed. It gives off a high pitched whine every now and then (probably the flyback transformer) but it doesn't do it often or long, and you occasionally have to hot-plug the ADB cord to get the keyboard and mouse to work after a cold boot but is otherwise a very happy machine.
It came with both the original CC board and the LC550 board. The LC550 board really makes it very pleasant to use.