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I’m working on two iMac systems both are the same model. They only will run in safe mode but won’t boot properly in normal mode. I’ve tried formatting the hard drive with an external usb and install a fresh copy of the OS.I’ve also change out the hard drive and re-installing the OS and that didn’t work either.I did a NVRAM and PRAM reset that didn’t do anything.I also ran it in single user mode and the fsck -fy that didn’t work either.I also have an OS-X server and ran it from the server and it did boot but froze.I did a AHT and nothing was wrongI also took it down to my Mac store and they ran a test and said nothing was wrong. Can someone help me please.

Do you have a bootable external drive? Does the system boot up via it? You will likely need to use the Option key to enter into there Startup manager to select it as the boot drive. Please review this: About the screens your Mac displays as it starts up What are you seeing when you start the system normally with the original drive installed? Update 3/20/19 Its time to pull the GPU board so you can check it out. Take a picture of the board and the heat sink before taking the thermal paste & pads off and post the pics here so we can see the interface surfaces. In addition take a good set of sharp pictures of the GPU board both sides after cleaning off the dust and the thermal paste. Lets see if we see anything thats missing our damaged. Adding images to an existing question