Possible PCI-e fault

I have a problem with my pc that I think I've managed to narrow down to a motherboard fault, but would like opinions from more knowledgeable people. Sorry for the length of this post. I want to be thorough in explaining the fault and the lengths I've gone to to diagnose it.

I've had this PC for about 3.5 years with no problems. The last upgrade I did was the graphics card, about 18 months ago.

Specs:

Graphics card: MSI GTX970 G1 gaming
Motherboard: Gigabyte Z87 GD-65 gaming
CPU: Intel...

Possible PCI-e fault