The computer shutting down is indicative of a power supply problem.
I know the Litepower isn't the best PSU there is but for what it's running it shouldn't encounter any issues. The only other components i have connected are 2 case fans, 1 cpu cooling fan and a 2usb hub case panel. The PSU is less than a year old so it shouldn't be suffering from any aging issues.
The thing that leans me away from a suspected power supply problem is that the GTX 770 runs fine and needs more power draw than the RX 570.
I can power the computer if I leave the 8 pin graphics power connector unplugged and run off onboard graphics. I believe it may be a fault in the graphics card, possibly a short within the card. I'll send it back for warranty though just to make sure.