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

[Vaer]

Check the CPU temp first by downloading a utility like coretemp or hwinfo, turn the game on and monitor the temperature. For hwinfo use the sensors table. If it rises really rapidly the heatsink might be loose.

If the entire computer is shutting down the cpu is probably getting too hot. According to the spec sheet, the cpu will automatically turn itself off at 71C/160F. The cpu is kinda weak so it might be fully loaded when running FFXIV.

It's also a possibility that you have a dud power supply but less likely since using the integrated graphics does the same thing. (That processor and a 560 let alone just the processor by itself is barely using an actual working 600-850W 80 Plus)

Check cpu temps first. If they are ok since you have an extra PSU I would try to switch to the other one. If all that doesn't work it might be the GPU. You can also remove the card and run it off the integrated for a bit and let it sit there to see if it is stable (it will lag but just check for stability/no crashing for a couple minutes) to check if it's the gpu.