My PC just stops and displays 'no signal' on the screen.
The power light on the on/off button goes out but the hard drive light stays on.
Also, the CPU cooling fan stops at the same time the power light goes off but the other fans keep running.
If I boot and go into the BIOS, it will keep running but if I continue with the normal boot,
it generally gets to around the login scrren before stopping.
It used to run OK and occasionally stop as described above.
As it is my home PC I just used to power off and reboot and it would generally work for another day or so - the frequency increased until now it won't boot.
I think that power problems can be discounted as it works OK when in BIOS.
I also think that the cooling fan can be discounted as it has good RPM and continues to run when in BIOS.
The CPU temperature is around 42 and system temp around 34. The shutdown temperature is disabled.
I think it may be a faulty CPU and would welcome any advice.

I have just booted into Safe Mode ok so guess it may not be the CPU??

Following your logic, you also need a CPU for the BIOS screen. There really isn't enough information to make a call on the problem, but I would guess you have a heat issue. Regardless of the bios settings, a system that is too it will shut down, lock up, or yield a stop error. My recommendation is to enable a shutdown for the default temperature threshold. Next, Power down and unplug your machine. Replace the heat-sink compound with a quality, silver-based compound (very small amount). Clean out all the dust, but first be sure you understand the dangers of Electrostatic Discharge. I use a compressor, but some use short bursts from canned air.

Good Luck

mb or PSU. Are you technically competent? Check PSU voltages at a spare drive connector plus at the big mb connector while the sys is running. Carefully.
42C is fine for a CPU.... 50C is not a problem.