That sounds like a good solution - if only I could find the damn service in the list

. It's an ugly mess of English and Danish titles and descriptions in there, but there definitely doesn't seem to be anything in either language that resembles "shadow copy", nor system restore.
The closest is probably Windows Backup (or Windows Sikkerhedskopiering in my Danish version, and the description does mention "restore functions"), but it's set to manual and isn't running.
... I ran a few Google searches, and it sounds like the Shadow Copy service is only present in Vista Ultimate and Enterprise? I'm running Home Premium, which - if I understood it correctly - uses some of the features from Shadow Copy for the System Restore function, but buried under some other services?