Something similar happened to me. I was playing crashdrive 2 and my mac froze on the loading screen, and it was also pretty hot. So I shutdown my macbook air and loaded it back up, but as soon as it turned back on the whole screen was grey,black and white with dead like pixles on it. I PANICKED! So my dad rang up Apple and they said that I would have to book a genus bar appointment. I was so upset and I only had it for two weeks. So I bought it into the Apple store and they technition said that I may have had my thumb in there or something. But I strongly remember just closing it and turning it back on. When the "genus" told me the price I was furious and I though how will my family afford this if it keeps happening. IT COST ME $600 AUSTRALIAN DOLLARS! Im only 12 and treet my mac like it's my brother and all my stuff is in great condition and I can use my stuff even after about 6 years. I never bash up or treat my stuff with disrespect and I rarely break anything, not even other peoples stuff. I am really annoyed with Apple for not just saying it was a faulty product, because I have an iPad, iPod Nano and an Apple TV and they are in wonderful condition, I also had an iPod Touch and it never broke or had a cracked screen, sadly it fell out of my mums bag when we were in a taxi and the person/people who came in after us may have saw it and decided to be dishonest and take it, and all of those products I had them for about a year and I still have my iPad and my iPod, and I got my Apple TV for christmas,still, that is longer than two weeks.
I love Apple products and refuse to use Windows, Samsung, Lg, Sony, Nokia, Telstra phones, Panasonic, etc, with acception of TVs, BlueRay players, fridges, mircowaves and other household appliances. ACCEPT SAMSUNG I will never use Samsung. If the happens again I won't bring it into Apple I will take it to a repair shop and they should give me a lower repair price.