My son went out of town and, upon returning, turned on his iMac. It rebooted and went into the progress bar typically showing during updates. It goes to the 50% mark, fairly quickly but then stayed there for 10 minutes. He rebooted and tried again but, this time let it sit overnight, at least six hours, but still stuck at 50%.
He tells me he installed Yosemite but not any time in the last few days before he left. From Googling around we tried resetting PRAM and also verifying the hard disk form disk utilities. The hard disk gave a green check mark(?) and said the volume was OK. I asked him to verify permissions but that was now grayed out.
Unfortunately, I am not a Mac user and I'm trying to help him over the phone. I'm very technically inclined but don't know what to do about this issue.
EDIT: So now things are getting worse as he tries rebooting and, after the start up sound, the computer powers down.
EDIT2: I just learned that the computer was not turned off while he was away which leads me to believe the system tried to update itself and something went wrong causing some system files to not be found or, perhaps, the few things we tried to do to the system helped that along.
So we found out Apple will check out his system even though it's not under warranty and, if it can be fixed in the software, they'll also fix it for free. What a great company!
EDIT3: Apple decided the hard drive had gone bad and replaced it. My son has a friend in the data recovery business who will attempt to extract the data.