Lay My Hat

This morning and this evening when I turned my PC on I got a whining noise and a screen which informed me the computer was turning itself off to protect itself from a serious error. The shutdown reports just note these incidents as 'blue screen'. I tend to associate 'blue screen' with 'of death' implying that the computer may go into blue screen mode and never reboot. Should I be worried or is it just a recent Windows update that could be playing havoc?

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what windoz system are you running? How old is the machine?
Were there problems before?
What other updates or files have you downloaded?
Noise could be something simple like the fan needs cleaning.

A few years ago my 2003 vintage desktop PC failed to boot and would attempt to start and then shut off again very abruptly. When I opened it I found that there was a plastic component (that was vital to the correct attachment of the heatsink and cooling fan to the processor) that had broken (probably due to old age). The PC was clever enough to recognise that the processor was overheating very quickly, thus instigating an immediate shut-down (while the fan ran at full-tilt). The replacement part was £3.95 on eBay. It's still working well.

One of the fans or the hard drive I'd guess. It's not clear from your description whether the error was reported by the BIOS or Windows. The BIOS would beep before shutting down due to a hardware fault. Windows would normally fail due to a software failure, which itself could be a bad hard drive. A failed fan on your CPU would shut down the PC shortly after starting as it doesn't take long for a CPU to get hot.

Probably too late to ask if you have a backup of all your data.

My PC (which is an all in one) had a clean not so long ago as it was overheating and shutting down due to dust accumulation. When that was occurring it booted up fine, but after a time of running it would just spontaneously shut down without warning. The current issue is not the same. This morning my machine started up without incident, but I am concerned that there is something lurking which needs addressing.

My machine is running Windows 7 and is about four years old. I have not installed any new software. Updates are set to automatic.

I would not be sure that the problem is not the same.
It could be anything, including more dust or just a component on the way out, loose connection.
It is time for visit to your local technician.