I have a similar problem, only worse...
I bought a Macbook Air on July 2014, but did NOT buy the extended Apple Care. On October 2015 the display simply stopped functioning one given morning. Not even the Apple logo appears when switching on the computer. The screen goes from pitch black to vertical lines varying colors from grey to light blue. This happened only 3 months after warranty expired. I've tried NVRAM Memory reset, but it had no effect.
As I am currently in Brazil working, I had to take it to the local technical assistance, which sent me a quote for nearly US$1,000 to replace the display. This is pretty much what paid for the whole computer when bought it in Boca Raton, FL.
Will Apple do something to replace it or will I have to simply abandon the Macbook Air? I'm not willing to pay so much to fix it and I find it absurd that this happened only 3 months after warranty expired. If it was a minor problem, OK. But the screen not working like this in such a short time is unacceptable.
The strangest part is that this happened the day after I updated the OS to the newest El Capitan.
Here are a couple of pictures showing what the screen looks like: