I'm trying to export a quick circle pattern I made in inkscape to use as my desktop wallpaper (Windows Vista ). I size the pattern to 100 x 100 px and export at 90 dpi. When I set the resulting png as the desktop wallpaper it is treated as 768x768 at 90 dpi. What gives?

Because if it were stretched to fit the width, the image would be deformed. Try making a rectangle with dimensions the same ratio as your screen resolution, centering your circle in the rectangle. Remove the rectangle stroke. Then Select All and do Fit page to selection, to make the image dimensions in the proper ratio.

But I want a small image that Windows will tile as the background. Instead of doing that, Windows is tiling it as if the image were 768x768. It's clearly not. It's 100x100. If I follow your suggestion I still end up with the single image that's centered on my monitor instead of tiled.

If I follow your suggestion I still end up with the single image that's centered on my monitor instead of tiled.

Well no, I don't think so. If you make the dimensions of the new rectangle the exact dimension of your screen res, yes. But note that I said "dimensions the ratio of your screen res". So your (screen width / screen height) x 100 = width, and height remains 100. Or something like that, sorry my math is a bit rusty.

But I think I do understand your problem. My solution will have your screen fully tiled, I think. But you'll have rectangles tiled rather than squares. And I'm not sure how to get squares tiled to form a rectangle.

After some testing, I'm able to choose a square image, right-click > Set as Desktop Background, and I do get the full screen tiled. In the Properties of the image I used, it says:
image width and height 58 px
vert and horiz res 96 dpi
bit count 8
frame count 1

I don't know if any of that pertains to the tiling or not? There are 2 different ways to make an image into your desktop (I'm on Windows XP Home) that I know of, and maybe more. Maybe that matters? How are you doing it?

The two methods I know of are:
1. Right click desktop>personalize>desktop background. This method does not recognize png as an accepted image format.
2. Right click image file (including png) and select "set as desktop background".

Either one gets the same result when I convert to gif in Gimp.

When I right click the image and check properties, it gives the dimensions as 100x100 but no resolution. I'm sure it's something to do with how I'm exporting since I remember reading about issues with that in the past, but I can't quite figure it out.