This sounds like it was all put in the case and hope it works. So back to the motherboard box with the motherboard in the box (it works as a test bench here) and just one stick RAM, the PSU, CPU+HSF and the video card. No drives are needed.

If that won't power up and stay up then we are done as we are looking at the possible bad part or parts. Most folk RMA that lot and start over.

If it does stay up then it could be a motherboard mounting issue. I still run into machines with extra motherboard mounting posts. And yes folk will argue it worked fine for days to years.