It's more than 10 years old. The graphics card has been replaced (with a used(?) one, so still more than 10 years old.
You continue to have similar issues with the replacement card.
You could try re-pasting the GPU heatsink (CPU heatsink, too, because you would be there, so why not?
If that does not help, then you might try replacing the power supply (it's more than 10 years old, so may have some failing components, maybe.) And, the logic board is more than 10 years old, too.
This all will be WAY easier to eBay a used, somewhat newer iMac, or get another mini, with a display that you like, or etc.
(It's not a simple plan to try to resurrect an old computer that is usually already retired by this time, and decide if it is worth doing)
You continue to have similar issues with the replacement card.
You could try re-pasting the GPU heatsink (CPU heatsink, too, because you would be there, so why not?
If that does not help, then you might try replacing the power supply (it's more than 10 years old, so may have some failing components, maybe.) And, the logic board is more than 10 years old, too.
This all will be WAY easier to eBay a used, somewhat newer iMac, or get another mini, with a display that you like, or etc.
(It's not a simple plan to try to resurrect an old computer that is usually already retired by this time, and decide if it is worth doing)