If you’ve got a 27” iMac from mid-2011 you’ll want to read this. Apple has started offering free replacements after it was found that some of the AMD Radeon HD 6970 video cards were starting to have issues, causing failures.
The affected models have serial numbers that end with DHJQ, DHJW, DL8Q, DNGH, DNJ9, DMW8, DPM1, DPM2, DPNV, DNY0, DRVP, DY6F, or F610. If you’ve got such a fault then you should contact Apple to get a replacement. Apple is offering replacements for these graphics cards at no cost for up to three years since the computer was purchased so you’ve got at least until May 2014 before you’re unable to claim. Still, it’s a good idea to replace it now than wait to see if it fails since it’ll harm resale value if you don’t.
Replacements for your iMac can be initiated through AppleCare, Genius Bars, and Apple Authorized Resellers. There’s no information on how long it’ll take, although it’ll probably be at least a week.