In Lesson #42, I removed the texture coordinates from the Quad in the upper-left viewport, and replaced them with simple vertex colors. Just like in lesson #1 or #2. When I do this, the quadrant is blank. If I try to draw any new objects in any of the 4 viewports, the viewports go blank. What's the trick here?

Have you disabled textures?
try removing the line in the code that enables textures or call glDisable( GL_TEXTURE_2D) after the initialization code.