The problem lies on the way the TD constructs the layout. Cells (or the HTML that defines cells) are not set with specific sizes, but rather made to fill the screen (using things like "width=100%"). Since cells are defined this way, the cell will take up only as much room as its contents need, and then IE will decide how to stretch the various cells on the screen such that the entire page uses up the entire window size (or screen size if in full-screen mode).
If a cell is empty, it will take up no space (or possibly just a few pixels in a particular direction - frankly I'm not sure how IE decides this). For example, start up the TD and don't load a tournament. You'll have basically no tournament settings and the default layout. Go to the Tournament screen and press "1" to display the main page. Notice the bottom and the bottom-right. The bottom is the Prizes cell, but since there are no prizes defined, there is nothing in the cell, and it takes up only a pixel or two in height. Because it is the only item in a row, IE still lays it out with the full width of the screen. In the bottom-right is the Chips cell, but since there are no chips defined, the cell is also empty. Notice that it is a few pixels taller (again, not sure why it's not 0 pixels tall, or why it's taller than the Prizes cell), and it is the width of the other items that are in the same column.
When you set a banner to "Stretch" mode, it sets the banner image's height and width to 100%. This means however tall and wide the enclosing element is. But since the enclosing element is also set to 100% height/width, we have a catch-22. How tall and wide should the cell/image be? Unfortunately, IE doesn't default to at least the actual size of the image, but instead it's as if the image is 0 pixels tall and wide. That's why if you use the Stretch mode, you must define the height and width of the cell explicitly. I believe this is documented in the user manual.
So basically you must tell the rendering engine how tall and wide to make the images. If you want all of your banner images to fit into a specific cell, set the cell's height and width. Then set each of the banners to Stretch mode.