It could be a bad component-video output on the player or it could be a bad component-video input on your display. Are you sure, though, that each cable is connected to its correct, corresponding input and output? Normally, an incorrect connection on your part results in a picture with no color (or very bad color). My suggestion would be to swap out units.
OK, I'm an idiot. After doing a little online research, I discovered that the upconversion button only works when the disk is stopped. After trying that, I discovered that I did get a picture for 1080 and 480, just not 720 (which is was set to for some reason). Thanks for the help.