You're a good man, Egon. You were right, the texels[] were black. I'm forced to use the following rather slow nested loop, but voilá, it works.
I think that I'm going to tackle a skeletal structure for it before I try my hand at a hardware renderer, but the eventual C# hardware renderer will benefit from direct access to OpenGL.
int i = 0;
for (int y = 0; y < image.Height; y++)
for (int x = 0; x < image.Width; x++)
texels[i++] = (uint) image.GetPixel(x, y).ToArgb();