iMac 27" (2010) Troubleshooting Tips - Confirm Dead GPU

Greetings folks, I'm looking to revive an old 27" iMac (2010) for my kids and could do with some tips and/or suggestions on the best way to troubleshoot the system and isolate faulty parts.

When I received the iMac I was told that the GPU (Radeon 5750) may need to be replaced. However, before splashing out on a new GPU I figured it'd make more sense to check the system over myself to confirm the GPU issue and make sure there aren't any others.

My troubleshooting journey so far...

1. I powered on the machine and it beeped once every 5 seconds which suggested there was an issue with RAM. It turned out that the issue was that it had no RAM.
2. I opened up the machine to check if any other parts had been stripped and found that it was also missing a hard drive.
3. After installing a hard drive and RAM I tried powering on the machine again. This time, instead of beeping the machine sounded the startup chime every 4 or 5 seconds. The fans were spinning, but the display was blank.
4. I tried hooking up a VGA monitor via the display port, but nothing showed there either.
5. I removed the GPU and the startup chime only sounded once, suggesting that the GPU may indeed be the issue. The fans appeared to run faster with the GPU out.
6. I looked over the GPU, but couldn't see any obvious signs of damage, however, when I removed the heatsink I noticed that the thermal paste and pads had dried out a bit.
7. I tried checking components for shorts with my multimeter, but I honestly don't know enough about GPUs to say for sure there are no shorts, just that everything I checked seemed to be okay.

Given what I've already tried, is there anything in particular I can do to confirm whether or not the GPU is dead?

Could it simply be that the LCD LVDS video loom cable is faulty, or something daft like that?

What other things should I be testing to determine if a repair is viable?

Here are some photos of the GPU...

https://postimg.cc/K32GZ4bd

https://postimg.cc/p9mXCgk1

Thanks kindly for your assistance.

Note: I'd sure appreciate it if you'd kindly refrain from providing unhelpful quips or giggling at the age of the system, she's a tad sensitive these days and prefers to be referred to as vintage rather than old, unsupported, discontinued or obsolete.