Your machine is out of warranty so what do you want Apple to do? When your car is out of warranty you dont get free repairs do you. This is why its so important to buy Applecare, it gives you peace of mind for three years. At some point all computers will go wrong, at some point all hard drives will fail, but for the small amount you pay you would have had help at this stage. I would advise to take to it a local Apple aproved service centre and see what they can do for you. In the mean time have you repaired your permissions, repaired the hard drive, done an SMC reset and tried resetting your PRAM? Also run the built in Apple hardware test to see what comes up.
Thanks for the advice, but I don't see how taking a patronising tone about hindsight is remotely helpful. And for the latter I'm not an IT technician, and haven't got a clue what you are talking about. I suppose the only advice that was remotely helpful was to take it to apple, However I loathe to pay apple a penny more!
And as for your analogy about cars, our last car a BMW (I would consider an equally reputable company as Apple) found a fault with the model which we owned, they wrote to us and recalled the vehicle and made the repair out of warranty. You only need to do a quick google search to see that this is a historical problem that Apple should be addressing.
If there was an issue with the 2011 iMac we would have seen a flood of complaints about it on the forum, since these contain AMD cards and I have a mid 2011 myself I would have spotted any major issues I would hope, other iMacs may have problems but I cannot speculate on that but as you were told this iMac does not, so there is no recall and hence no out of warranty service. Graphics cards can go wrong, if that's happened im sorry but without Applecare you cant do much. As to the other things mentioned you could have tried googling for them, or searching the boards, they are trouble shooting steps to try on Macs. As to 'Historical Problem' No its not, well not on the 2011 model, there was a hard drive recall by Apple all the way back to 2009 if you had a certain hard drive, and that's good service because those machines were out of warranty. Don't try and link one thing to another and expect it to be a recall issue when its not.
As to my tone when looking for help saying 'lets moan about Apple' isnt going to get you to far on an Apple help forum. Here are some links that may help. SMC reset http://support.apple.com/kb/ht3964 PRAM reset http://support.apple.com/kb/ht1379 Permissions repairs http://macs.about.com/od/applications/ss/firstaid.htm Oh and check here to see if your iMac needs a hard drive replacement. http://www.apple.com/uk/support/imac-harddrive/ I hope this helps.