Orbital Shark, where you have that button that says "TV Settings" I have "Power Settings". I think this computer recognizes itself as a laptop display, so that could be why.
Well, I contacted Sony Support and they were no help at all. They just couldn't figure out what it was that I wanted to do. I finally gave up on that, and so I'm going to stay open to more suggestions from you guys, if anyone has any. I'm also going to try taking pictures of what this display is doing, compared to what I want it to do, just so I can confirm with you that I'm using the right terminology to describe all of this.