Posted here for my own reference for the next time it happens; occasionally, the icons on my Mac refuse to drag anywhere. Which is a bit weird. Binning the cache and preferences files listed in this post, then logging out and logging back in again, solves the issue.
Oh, and trashing QuickSilver's prefs fixes the problem where it disappears as soon as you invoke it. Yes, I have filed a bug report about that.
Shock! Mac OS X isn't completely hassle-free! Gasp!
Turns out the can’t-drag-Finder-icons problem is also a QuickSilver bug, that’s been open for about 18 months. I’ve even left notes in the bug tracker thread. Weirdly, QuickSilver is very well-behaved on my desktop Mac, but seems to take an instant dislike to my PowerBook. I’m ditching it and going back to LaunchBar again, I think.