PC works for a while then dies

I built a new PC and everything worked well for a while until one day it just died while mid-game and wouldn’t turn back on again.

The psu was one of those that came with the case so I figured it was that, bought a Corsair one, refitted it and then it was that the fans would spin for a few seconds then go off and then it would repeat the cycle over and over.

What’s really weird is this is a second pc I built from some "extras" I had after upgrading my main PC so I put the processor back in the main one and it booted fine but just to try the motherboard, I put my new processor in the second PC and turned it on. It booted. It ran for about 10 minutes then shut off again and is now back in the same cycle of fans running then rebooting itself.

I’ve also changed the power lead and used a different extension lead in case it was one of them.

After much frustration, I realised that as the case doesn’t have a speaker, I wasn’t getting any POST beeps so I connected a speaker and got none. Took out the memory and tried again and got no memory beeps. Put the memory in, tried a different stick, tried both slots on the board, all to the same result. I put both sticks in my main PC and ran a memory test which came up clean.

The memory is 2400Mhz and 3000Mhz. The motherboard only supports up to 2666Mhz according to the specs so I’m all out of ideas.

I can only assume that the slots the memory goes into are in some way faulty. Unless there’s anyone with any other ideas.