Apple - Thin green lines on boot, then screen goes grey (late 2011 MBP – 8,2)?

You may be suffering from a known graphics card issue. The good news, if you are, is that Apple will cover it via a repair extension program:

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.