A few weeks ago, my MacBook Pro 2011 Early started to behave strangely. It started right after I had upgraded my system to Mavericks. I was testing the new iMovie as I was getting a black screen (of death). After a hard reset, the the grey boot screen (with the Apple logo) looked scrambled with strange line artefacts. And the machine refused to boot. I managed it to get the machine working a few last times (doing 100 reboots and trying out all boot options), but finally the machine was dead. It was clear, that the discrete graphic card has a problem. And so, the only solution was to replace the hole logic board.
So I went to the Apple Store. I had to wait 1.5 weeks to get my MacBook back and the price for it was 490€.
A quick look into the internet reveals: Apple has a problem. It looks like the number of melted MacBooks from 2011 is fast increasing:
My flatmate, who also owns an Early 2011 MacBook, saw his MacBook fried this morning and is on his way to the Store now.
There is hope that Apple will announce an official replacement program in the future (and give a refund for the repair costs), but until then you have to pay the replacement yourself. But if you do, tell the Apple Staff that its a really common problem and their should do something about that now.