Hi everyone. I am working on a 2011 27" iMac for a customer, and it has me stumped. It is behaving very strangely, and I can't really figure it out. The primary issue is when the computer is booting. It will start to load macOS, the restart after a while. The progress bar never gets much past halfway. The computer had issues a while ago, and the customer took the machine to Best Buy, but they were told that the machine was too old to repair and were pushing her towards a new machine. She brought the computer to me, and I have been looking at it today. The specs are as follows (as best I can tell):

• Intel Core i5-2400 (3.1GHz QC)
• 4GB DDR3 (1333MHz, 2x 2GB)
• 1TB HDD
• 1GB AMD Radeon HD 6970M GPU (Possible culprit?)
• macOS High Sierra 10.13.x

I have spent a while trying to get it to do anything productive, but haven't been successful. Here are the things I have already tried:

• Reset SMC (did nothing)
• Reset PRAM (did nothing)
• Boot from USB SSD with 3 different operating systems on it (starts to boot, then freezes and restarts)
• Boot into macOS Recovery (wouldn't work)
• Boot from USB macOS High Sierra install disk (didn't even see the disk)
• Boot from Internet Recovery (took a while to load, ended up at a grey screen)
• Boot into Target Disk Mode (worked and can access data on the hard drive, but doesn't help me fix the iMac)

Does anyone else have any ideas about what I can do to fix the computer? It is a really nice machine, and the customer would really enjoy being able to use it again. Any help is appreciated.