Apple told my wife this iMac was "Unfixable"...did they LIE???

2011 iMac with an AMD Radeon GPU, Intel i7 Quad Core. It overheats and shuts itself down after being on for a minute. Then it goes into a never-ending boot loop. Furthermore, Apple stopped supporting this model and you can no longer update the iOS. Let's see if there's anything we can do to make it a working machine...
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