Problem Solved
I had the identical problem. I downloaded Yosemite from app store, began installation, and after required restart apple logo would appear and it would begin to load and I saw the installation bar begin to move and show percentage of installation--then when it got a quarter of the way installed the screen switched to a blank white screen and sat like this for a day! I tried everything, unplugged, forced reboot, power on and off, etc.--all with same results. Then I did hard power off and on and entered safe boot mode. Here's how to do that:
Be sure your Mac is shut down.
Press the power button.
Immediately after you hear the startup sound, press and hold the Shift key. The Shift key should be pressed as soon as possible after startup, but not before the startup sound.
Release the Shift key when you see the Apple logo appear on the screen.
Eventually the computer did enter safe boot mode and once it did it finished installing Yosemite. I then, based upon what I'd read on this page, repaired all disk permissions and then when that was finished and the installation was finished restarted the computer and that worked and all was good in the hood! Hope this saves everyone the aggravation and madness I went through on my end for the last 3 days. Thanks and good luck!