Hello and welcome to the forums!
First off which model of 850 Gold PSU are you running, we make a few different series's. 
 
I would start with opening your case and retrying, see if there is anything major such as components feeling unnaturally warm or any odd smells.
As long as that is fine, I would then pull everything off that does not need to be on to power the system.  Power the Radeon and the EPS on the motherboard and try to POST and go into BIOS/UEFI.  Once there go to the monitoring section and watch voltages and temperatures.  If everything looks good, try to leave it there for a while and see if it stays on.
If it does not stay on, the try removing all of the cables and inspecting both ends of the cables as well as the plugs on both PSU and device side, I recommend using an LED flashlight as the white light  tends to not distort color or cause as much glare.  See if anything looked damaged in some way.  If ti does, let us know, if it does not, reassemble and retest.  If the issue persists try swapping cables, for example if your motherboard only uses 1 EPS, try a different EPS cables and a different EPS port on the PSU, same goes for the VGA cable.  This will become a bit of trail and error to isolate the issue.  I did deal with something similar to this several months ago, and in my case, I found it was one of the 2 EPS connectors on my motherboard that was causing it.
 
I know this method can be a bit cumbersome but it is typically very effective and will allow you to isolate the source of the problem.

hmm.... having the same issues as you both for the past couple months.
 

If anyone found a solution or even ANY more info about the PSU acting up, please post it. It's never helpful to leave a thread twisting in the wind like this.

I ended up RMAing the psu.  Everything I tried was dissconnecting and reseating all connections. The paper clip test with the supplied psu tester that came with the psu, and I ran voltage checks with HWmonitior. None of these thing seemed to help me figure out what the issue could be so i'm hoping I wont have this problem anymore once the new RMA psu comes.  Once I get the new psu I will post on wether or not I'm having the same issue. Cheers

Same as I with EVGA GPU when Pascal show up.
Only I would use fire because I want to suffer and melt in front of my eyes and camera.
I don't like when someone destroy hardware, I can't even look when someone destroy new things, but for this card I will enjoy.
 
Only you made mistake because didn't give them one chance to replace 850 G2 or you should immediately to go on 1000 P2.
He have better customer score than HX1000i and cost same and Super Flower is better than CWT.

Vlada011
Only you made mistake because didn't give them one chance to replace 850 G2 or you should immediately to go on 1000 P2.
He have better customer score than HX1000i and cost same and Super Flower is better than CWT.

I've got to agree with Vlada011 - EVGA has the best customer service of any computer company I have seen - hands down.  At a minimum I would have contacted support and requested an RMA!  My experience with them has been that their support answers in under 4 hours - and their RMA process is painless.