So your opinion is the GPU is dead along with the hard drive?
If you are seeing artifacts on the screen, then the GPU is most likely failing.
HDDs are weird. I have had HDDs that were in the process of failing for literal years. Sometimes I start to see symptoms and the HDD would fail in weeks.
So, even if you HDD is starting to go, it doesn't mean that it is bad and may go one working for a long time afterwards.
Could you take a picture of what the screen looks like with the artifacts?
If by any chance the GPU is still hanging on, you can test to see if the HDD is the culprit by booting from an external drive.
There is also Apple's HW Diagnostic Tool, you hold the "D" button right after the chime during boot up to start the tool. The bad news is that I often get false negatives using the tool.
For example, the tools says the HW, including the GPU, passed the test, but I see artifacts on the screen while the test is going.
I never had a false positive though.
If you do the test, let us know the results.
The hard drive is a difficult but doable fix for me but I am not sure about the GPU.
The GPU requires the removal of the logic board which most would probably agree that it isn't a novice level of work.
That said, with the many guides, YouTube videos, how-tos, and forums to help you, I think even a novice could do it fine.
In addition to a new (or working) GPU, the job also requires adding new thermal paste and pads, but this really isn't that big of a deal.
If you don't think this is something you can do, I suggest giving it away to someone you think would be interested getting it working, or just trashing it. The last part always makes me a little sad to say.