It's a Windows 10 PC, a few years old but high spec when I bought it, Core i7 processor, 6GB of Ram and a Radeon R7 370 2GB graphics card sitting in a PCI Express slot.
This morning I opened the case, gave it a bit of a hoovering and checked for loose connections. Nothing obviously so I switched it on and it booted up. The only thing I could see that concerned me was that the two fans on the graphics card weren't running, even though the heat pipe below them was getting pretty warm, maybe 50 - 60 degrees. Tried re-starting Windows to get to the Bios settings and its dead again. Back to what was happening last night, which is that it starts up, all the fans, disk etc whirring away then after about thirty seconds there's a gentle "click" and all stops. Pause for a couple of seconds then the thirty second sequence starts again. This problem started after the PC had been on for over an hour, so now I'm thinking that it might be the power supply overheating.