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.
You didn't post what model set you're using but my guess would be that it won't accept a 720p scanrate, hence no picture when you set the Zenith to 720p.