iMac booting to external drive

I've been asked to take a look at an issue for a friend and I don't think I'm getting the whole story but here we go...

It's not booting to the internal drive it's booting to a connected external drive. It looks like they setup a daily backup via Carbon Copy Cloner to this external drive from the Macintosh HD. The Macintosh HD is no longer there. I can't see it in the disk utility or in the recovery utility. The only thing available in the recovery utility is the external HD and Disk0 with OS X Base System under it. It seems that the Macintosh HD is gone. I have tried many different tasks to "see" the Macintosh HD and still no joy. Is there any way to identify the internal HD and perform a recovery from the CCC to the HD to get this Mac booting back up to the internal drive and not the external one?