Sounds awfully similar to a problem I had with EVE a couple years back. Thought my Gcard was busted, but it turned out to be the Power Supply.

And when I say similar, I mean virtually identical, right down to the screen going random color blocks.
Initially replaced the 980Ti was using (it had a fan malfunction the previous year, repaired under warranty) thinking it was the Gcard failing again, but continued having the problem.
The PSU I was using was pretty old, but it was a 1250w, so I had more than enough wattage. The problem was simply that due to age and general breakdown, the PSU was fluctuating its supply to the PC.

So my recommendation is to try a new PSU.
Also, its possible to still do the free Windows10 upgrade if you can find the relevant links. Which I would recommend, since previous versions of Windows have had their support dumped by a lot of places.