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The graphics card is kaput on my refurbished 2011 27” iMac. I’ve been told that Apple no longer make graphics cards for this particular model. Is there either an equivalent spec card that can be installed, or can these cards still be found online ? The hard drive was replaced one year ago.

Your machine uses a 27” iMac AMD Radeon HD 6770M 512MB Video Card Apple part# 661-5967 There was an Apple replacement program on this card several years ago, so it’s a known issue. Replacement can be found but are high due to supply and demand. I have had a 70% success rate doing a hot air work station reflow of the video card. This repair guide is for the 2010 but will fine for you: iMac Intel 27" (Late 2009 or Mid 2010) Graphics Card Replacement