Computer Help Please! My computer keeps crashing after installing new GPU.

[Nedkel]

I think one thing that is going on here is a failure of your motherboard.
If you couldn't have an RGB light with 600W PSU then there is something cheesy with it, maybe draining too much power for some reason, maybe it has too old capacitors which don't hold the voltage too well. If it would be the CPU overheating, then the system would just shut down itself, and if it would be the graphic card, your game would be still running and you would be able to hear the sounds from the game. It may be that motherboard is rusty somewhere or cracked, drains more power and in result overheats in one part or another. Probably also your GPU contributes to your problem, it may drain too much power out of PCIE slot and this could be really heavy on your motherboard power section.

Its a time to change motherboard, CPU and Memory to DDR4, my guess is your setup was never designed to have high power GPU in it and play games, its an office computer made into gaming which never ends well.
I would recommend for you to get i5-9400f with B365 motherboard or Ryzen 5 2600 with B450 motherboard.