Just had similar symptoms of failure with my 2011 MacBook Pro a few weeks ago: 15", i7 2.3 Ghz, AMD 6750M
The Mac would not boot and would stick on the grey loading screen, the only way to boot to desktop was with Safe mode. This pretty much made the mac unusable even for just email or web use never mind graphics and video editing work.
And even worse this was 18 days after the 3yr Apple Care expired . Tried a clean backup OS system off a external drive same result.
Took my MBP to the Apple Store for a Genius appointment (Hong Kong) first chance I got, the genius I spoke with was very fair and professional and took my MBP to the store workshop to perform some tests (OS, ram etc) and returned saying he was unable to boot the mac at all. A logic board replacement was prescribed at the cost of $4500HKD ... I had by this point presented a slew of reports of the GPU failure in the 2011 model off my iPad (and later the genius admitted seeing more than a unusual amount of this 2011 models coming into the Genius bar).
Fortunately for me the repair fee was discretionarily waived by the manager on account of both the geniuses recommendation and as I had previously taken my mac while still covered by warranty to a Genius bar 6 months earlier and mentioned symptoms that the mac screen was blacking out and shutting down which were unable to be recreated at the time. Some faith in Apple restored!!
Having had my MBP back with a new logic board it seems ok so far, completed some initial CPU intensive processor tests at 100% = 90℃/ fans 6000rpm under load of video transcoding but dropping back to a average of 60℃ and 2000rpm when idling at 5% CPU. Hope this replacement logic board wont fail when out of the 3mth warranty as other have reported. Selling this machine on as a ticking bomb to someone else seems like bad karma ☯.
Appleplease acknowledge the flaw in this premium computer and begin a official recall programme.
* Coincidentally I had already been following the infamous MBP2011 Apple Discussions thread as my friend had his MBP2011 die on him in early April, he ended up paying for a logic board replacement in Amsterdam. And another friend who works as a designer just had his company MBP2011 die the same week as mine in London.