iMac Gray Screen on Startup

2011 iMac running El Capitan

It appears to boot up normally (chime, apple logo, progress bar), but after the progress bar goes to a solid gray screen that will not go anywhere. At that point the only option is the power button to power off.

Trying to start it in safe mode has no effect.

I have started in Recovery mode using cmd-opt-r, and I get the spinning globe with its progress bar, but when that is complete, it goes to the apple logo with it's progress bar, which again leads to the solid gray screen.

I have a time machine backup, but no way to get to it since Recovery mode won't work. Is this indicative of hard disk failure?