Q: Yosemite boot progress 40% and then iMac turns off.

I'm in a bit of a pickle here. Lately I've been experiencing irrecoverable freezes which force me to do a reboot from the power button. I hate that, but I can't find any other way to get out of the freezes. Sometimes the mouse works but it can't click on anything.

Anyway, today I had to do it again and when it rebooted, it proceeded to about 40% progress when it slowed down for a while and then literally shut the computer off.

I tried it in Safe mode and the same thing happened, only quicker.

I don't have any external drives connected. I have a 3TB "Fusion" drive. My iMac isn't new but it's not that old either. No DVD drive. 32MB of RAM.

I've zapped the PRAM, or rather the NVRAM it's called now.

I've run in Internet Recovery mode to no avail.

Any theories?