Repairing a broken OSX.
There have been reports of OS X Yosemite freezing after a software update. This can happen to any version of OS X. If your Macintosh won’t boot up firstly I’d leave it a few hours, maybe even overnight, and see if it comes good. If not, you should ring Apple as they will be able to talk you through how to fix it. Otherwise, if you are outside of your Applecare, or want to have a go at it yourself, here’s what I’d do.