Got my laptop home again, with a new logic board covered by Apple Care.
Backed everything up with Time Machine. Decided to get rid of Windows XP, since I rarely use it and it takes up >35 gigabytes of space. Found I could do that without uninstalling VMWare Fusion, which seemed handy in case I ever want to test some other operating system. Backed up again. Re-installed system software, since that had been suggested by the Apple repair team. Ran many updates. Backed up again. Also backed up with Super Duper.
My laptop is now backed up to two different external drives, running an up-to-date version of Snow Leopard, with 41 gigabytes of free space. Boring but necessary maintenance. And I'm so glad that everything is now fixed and working properly.