So what exactly is wrong with it? Does it work fine for a few mins then shuts down? Do you get any visual on the screen?
The H.U. illumination probably doesn't mean much as that's controlled by the headlight switch in the car; different circuits etc.
The CCC has several components, including ram that could be bad.. Have you pulled the unit out a bit to see if touching any wires in the back yields any difference?
Have you tried the CCC hard reset [for when it's locked up]? Press the eject buttons on both the dvd-drive and the cd-drive, while holding press the volume/power/mute button. That should reset the system.
Try unpairing and unplugging all devices when it is working and see if that yields any difference, an old co worker had consistant lockups on the CCC when his blackberry was paired to the car. Unplug iPod etc.