Given the age of your system I would bring it back to Apple as this would be covered under warranty.
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The display cover glass is now a sealed with the LCD panel (thin series) unlike the older iMac's. They are not designed to be taken apart and in doing so you run the risk of breaking it!
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The display cover glass is now a sealed with the LCD panel (thin series) all one unit, unlike the older iMac's. They are not designed to be taken apart and in doing so you run the risk of breaking it!
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Here's the IFIXIT guide on taking the display off but even still you would need a new one to replace yours. [https://www.ifixit.com/Guide/iMac+Intel+27-Inch+EMC+2639+Display+Replacement/19632|iMac Intel 27" EMC 2639 Display Replacement]. As you can see even this is a big job.
Given the age of your system I would bring it back to Apple as this would be covered under warranty.
The display cover glass is now a sealed with the LCD panel (thin series) unlike the older iMac's. They are not designed to be taken apart and in doing so you run the risk of breaking it!