You know, the "no HD found" might actually be the EXACT same problem as the power loss and battery icon.

See, if there's not enough juice to spin up the drive, then it would give you that message.

The fact that the player boots fine under AC adapter power means that the problem is definitely external to the player: Either in the sled wiring or in the voltage the car is supplying to that wiring.

Maybe it's something as simple as a swapped ignition/constant wire? Or a blown fuse somewhere?

In any case, I'd say it's time to triple-check the wiring.