To determine if it is your hardware or OS X boot from external drive. If it works it is your OS X, if not, it is your hardware.
If it is OS X use Safe mode and:
- look for non apple drivers loaded using
sudo kexstsat in Terminal (enter password)
http://www.apple.com/support/macbookpro-videoissues/
Apple has issued a Repair Extension Program for Video Issues. I was experiencing the same problem and had tired several solutions that worked for a short period of time, but ultimately I was unable to get my MBP up and running last night and brought it into an Apple store. They determined that my issues was in fact a video issue and qualified for free service.
If you purchased a MBP between February 2011 and December 2013 and suspect that your MBP is experiencing the same issue, then check out the page URL above to see if your MBP qualifies for service.
Here's an excerpt from the page
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Apple has determined that a small percentage of MacBook Pro systems may exhibit distorted video, no video, or unexpected system restarts. These MacBook Pro systems were sold between February 2011 and December 2013.
Apple or an Apple Authorized Service Provider will repair affected MacBook Pro systems, free of charge. See below for details on affected models and service options.
Symptoms
An affected MacBook Pro may display one or more of the following symptoms:
Distorted or scrambled video on the computer screen No video on the computer screen (or external display) even though the computer is on Computer restarts unexpectedly
Products affected 15-inch and 17-inch MacBook Pro models manufactured in 2011 15-inch MacBook Pro with Retina models manufactured from Mid 2012 to Early 2013
Best Answer
If your Mac shows a white screen in recovery mode or internet recovery then there is a hardware issue on your mac.
My recommendation is to either contact Apple Support for an appointment or set up an appointment yourself via https://getsupport.apple.com/.
This could be a hard drive or display issue. If not then you are looking at a logic board replacement.
If you have a time machine backup or a separate backup of your things elsewhere then you should be fine, if not then you'll want to get the hard drive (if that is the issue) taken out and then purchase a new one, so you can take your current hard drive to the nearest data recovery center nearby you.