What's wrong: Radio only clicks via speakers when turning on/off. No other sound.

[PoisonIvy]

Like MetroMPG said, if you're getting a bit of an electronic pop from the stereo it's getting power. And if you're getting power, it should mean the factory wiring harness is plugged in properly. And the speakers are obviously picking up something. It's likely the stereo is just toast. Since you'll need to pull the stereo anyway to either replace with a used factory or an aftermarket, take a look to make sure everything is plugged in tightly behind the stereo.