Comment 2 for bug 408592

1. Right-click a blank area on your desktop.
2. Click Properties.
3. Click on the 'Themes' tab (leftmost tab)
4. Click the dropdown box under 'Theme:'
5. Select a theme (other than WIndows Classic), then click apply. It goes live immediately.
6. Run Inkscape. Try a 'Save As' operation.

Sorry for not including these steps in the OP.
I just remembered that I'm using a 'modded' version of XP, that comes preinstalled with some 3rd party themes (Royale themes, IIRC, I'm not at the offending computer). Perhaps that the source of my troubles.