I've resolved this problem…after reading loads and loads of other threads. It was a problem with the dedicated AMD GPU. The solution was to force the computer to use the Intel graphics processor rather than the dedicated AMD graphics processor. I can't tell exactly why my AMD processor stopped working but from what others have said it appears the problem could lie with the lead free solder used to attach the AMD processor to the motherboard i.e. it wasn't ideal and tends to fail.
The solution that worked for me, and it appears that different people with roughly the same problem have found slightly different solutions, was to move the AMD AND ATI processor extensions out of the System/Library/Extensions folder and place them in a newly created DisabledExtensions folder. This is done using the Single User mode (with your computer off, hold the command and s buttons and press the power key to turn the computer on. You have to be very careful doing this because you're editing code and to would be easy to screw things up.
The discovery I made, which made my particular solution work, was that apparently identical MacBook Pros (Early 2011) can use different AMD processors. So the first solution I found, which looked to be perfect for me, wasn't because I didn't have the exactly the same extensions - the solution required me to type in four named extension.
On first try I managed to progress as far as the instruction which asked for the extensions to be moved, but I got a response saying "file does not exist". On further investigation I found another thread which suggested using a slightly different command which moved any extensions which started with AMD, but didn't need to precise extension name.
To put this all into context, my MacBook Pro is as follows:
MackBook Pro 15" Early 2001
Processor 2 GHz Intel Core i7
AMD Radeon HD 6490M 256 MB
Serial Number beginning: C02F…...
The first set of instructions I found was a YouTube video here:
https://www.youtube.com/watch?v=iyDu-Y_G1D8
This contained the following Single User mode instructions:
fsck -fy [once this file check has run and come back saying "The volume Mac HD appears to be OK" move to the next instruction]
mount -uw / [return]
mkdir /DisabledExtensions [return - this creates the folder the extensions will be placed in]
cd /System/Library/Extensions [return - this takes you to where the extensions to me moved reside]
The next command is were is stopped working for me. The next command wants to move specific named extensions, which I clearly didn't have in my Extensions folder. This fix I found was, as stated above, in a command which simply moves all extensions starting with AMD. This fix is here:
2011 MacBook Pro and Discrete Graphics Card
The next command I used was:
sudo mv AMD* / DisabledExtensions/ [return]
However, there's a bit of a contentious issue in the Discussion Forum page listed above. There are some post saying that you have to move the AMD extensions AND the ATI extensions. There are also some posts rubbishing this, saying that you don't need to move the ATI extensions. I certainly needed to move the ATI extensions, because I got to the end of the original instructions - which I'll detail below - rebooted and it hadn't fixed the problem.
So I found another web page which listed the precise extensions that needed to be moved for my particular AMD Radeon HD 6490M processor, and it listed the ATI extensions. So I went back in to Single User mode and added:
sudo mv ATI* / DisabledExtensions/ [return]
I then came back out with the remaining commands from the original video instructions:
cd /
sudo touch /System/Library/Extensions
ls /DisabledExtensions [return - this lists the moved extensions but it's l as in lima, not a cap i:]
reboot
And it worked. As various people have stated, this is a workaround and not a fix. You're now using the onboard graphics processor, which is OK but doesn't run video very well at all, has trouble with certain web pages and means you can't adjust the screen brightness. And you can't use an external monitor…although I haven't been able to verify this.
So if, like me,you have an AMD Radeon HD 6490M processor, try this in Single User mode:
fsck -fy [once this file check has run and come back saying "The volume Mac HD appears to be OK" move to the next instruction]
mount -uw / [return]
mkdir /DisabledExtensions [return - this creates the folder the extensions will be placed in]
cd /System/Library/Extensions [return - this takes you to where the extensions to me moved reside]
sudo mv AMD* / DisabledExtensions/ [return]
sudo mv ATI* / DisabledExtensions/ [return]
cd /
sudo touch /System/Library/Extensions
ls /DisabledExtensions [return - this lists the moved extensions but it's l as in lima, not a cap i:]
reboot
I hope this helps. I'm off to the local Apple store now to see if I can get a permeant fix under Apple's MacBook Pro Early 2011 AMD Replacement programme.
Regards