To MaryonSketchup:
From the picture you provided, it looks as if for some reason the edges of that rectangle are not on the same plane as the rest of the flat face. These edges may be "microscopically" separated from that plane, and I do not believe even using Intersect Selected will change that.
So apparently you have a faceless rectangle, which may even be slightly twisted. Try drawing a diagonal in the rectangle.
Of course, I may be missing something in the information. You could also upload a copy of your file in much the same way as the image.
Only meant to assist.
mitcorb