I found
OS X Yosemite: If you see a gray screen at startup but I don't think that it's very helpful. It says nothing about hard drive failure (which is a possibility in your case). See if any of the links at
this Apple support page help.
As Jon notes, hard drive failure is definitely a possibility, but you need to rule out other possibilities with the various steps I've described above. If you have either TechTool or DiskWarrior, those can be run as well - either from your backup drive (assuming you've got them installed and assuming you can actually start up from your back up drive) or from a CD if you have a CD drive.
In addition to hard drive failure, it's also possible that there is some other mechanical/electrical issue. My son's girlfriend's MacBook Pro recently started behaving badly - somewhat similarly to what you're seeing. I suspected hard drive failure as we were able to get it to start from an external drive. So we got a new drive and my son installed it (yay...finally got him to learn to do that sort of stuff without handing it over to Mom!!) and still no joy. At that point I started wondering if it was a cable, since it would work from an external drive. Hoping of course, that it wasn't a logic board issue, as she has no spare cash and that's an expensive repair. They took it in and I was right - it was the hard drive cable. While not cheap ($169 for diagnosis and repair) it was a heck of a lot cheaper than a new logic board or a new Mac!!!
Next time I think I've got a dead drive on my hands I'll try to remember to test the darn thing in an external enclosure before jumping to conclusions. On the upside, she now has 2 backup drives - I made her buy one immediately and now she's got the old internal as well - one for TimeMachine and one for CCC.