MacBook – diagnosing (likely) hardware fault on MBP 15” (early 2011)

Today while I was routinely using my Macbook Pro 15" from early 2011 (model MacBookPro8,2), running Mavericks DP3, the screen suddenly went all glitchy and distorted and the system locked up. (I just mentioned the OS for the sake of completeness; I have a strong feeling that it's a hardware problem and has nothing to do with the OS.)

After forcing a reboot, I got the gray screen with the Apple logo and the spinner – except the display wasn't quite right: the entire screen was distorted by narrow white horizontal lines running across it. After a while the screen would transition to a purely gray one and the system would be nonresponsive (without ever having reached the login screen). After rebooting several times with the same result, I tried the different startup key sequences. I was able to reach single user mode (CMD + S) where I did fsck and the hard disk seemed to be OK. (FWIW, in text mode, the screen appeared normal.) exiting after the HD check didn't do any good though, and the system hung up again.

In the end what appeared to help was pressing the Shift + Control + Option + Power Button key combination (related to resetting the SMC) on the aforementioned pure gray screen, which would cause the system to instantly switch off. (Note that I did it while my system was already running, even though the procedure outlined by Apple requires that it be done while the computer is off.)

Upon turning on the laptop, the screen looked normal again, and the system booted as usual and I was able to log in. I was able to use my laptop normally for a couple of hours when suddenly the screen went completely red as I watching a video online. Force rebooting led to the same problems again, and I was able to "fix" it again, same as before – except this time round it only worked for a few minutes before the problem recurred (this time initiated by the screen turning a pure blue).

Since then I've only been able to use the system for a few minutes before the problem reoccurs.

Question is, how do I go about diagnosing the problem? (I suspect it might be a problem with the GPU or RAM.)

I couldn't get into Apple Hardware Test (AHT) even though I tried pressing D during startup. Apparently it's not there for systems running OS X 10.8.4 and above (I read that in one of the Apple docs although I don't have a reference to it this instant.)

Any help would be appreciated.

Edit: I should mention that the fix (i.e. the keyboard combination) doesn't always work the first time. I don't really know if pressing that particular combination actually helps at all – maybe it just randomly works after "turning it off and on again".

Update: I think the problem is related to the discrete graphics card (The AMD Radeon HD 6750M). I installed a free utility called gfxCardStatus that lets you know whether whether the integrated or discrete graphics chip is being used, and also lets you manually set it to one or the other. As soon as I set it to the discrete chip, the screen when all blue and liney on me, and after I force-rebooted I got all the symptoms of my problem.

The great thing about this little utility is that it lets me disable dynamic switching of the graphics chips and set the graphics to use the integrated chip. This means that my laptop should at least be usable until I'm able to get it fixed.

I'll be Googling on this issue later when I have time – a quick search showed that other people with the same MBP model as mine have also reported problems – but I'm still looking forward to suggestions here. Thanks!

Update 2: I think I was a bit hasty in pinning down the fault on the discrete graphics card. As I just found out, the problem can also be triggered when switching to the integrated graphics card, or may not be triggered at all by switching – I was able to switch between integrated and discrete without problems one time.
I guess that the most that can be said right now is that the problem is with something in the graphics subsystem, and that it is possibly triggered by the switching from discrete to integrated graphics and vice versa.

Update 22nd Aug, 2013:

I took my MBP to an authorized service center where I live currently (in the Middle East) and they diagnosed the GPU as faulty, which is what I (and others here) had suspected. They said they would have to replace the logic board, which would cost the equivalent of over $1000 US. Doesn't seem to be worth it as I can buy an 11" version of the latest MacBook Air for slightly more.

Unfortunately, I'm no longer able to successfully apply my previous "trick" of force rebooting several times until the display comes up normal; it doesn't work anymore, after trying dozens and dozens of times. I just get the start-up chime, with the faulty display, followed by a blank gray screen.

If I boot up in Single User Mode (Command + S), the display begins to run normally, which I suppose is because it uses the integrated graphics card (just my guess). But that's the best I can manage; I'm no longer successful in getting it to boot so I can force the integrated card to be used (via the gfxCardStatus app).