Thankyou for your help so far.
I have just done some more testing and I can confirm that when in BIOS if SOPB (I will call it from now on [Soft Off Power Button]) is set to 4 seconds and I hold in the power button on the tower for those 4 seconds the computer correctly shuts down.
If, however, the SOPB is set to Instant Off and I press the power button on the tower it will turn off instantly and restart after ~~5 seconds.
This may be iteration, but it is now a fact.
Also, DM, I have looked in my BIOS and there is no EuP or Energy using Products option.
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Is there anyway I can tell the OS's shut down function to do whatever the system is doing after holding the power button in for 4 seconds?
It is like these are two different functions.
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EDITED: I previously said:
"Also, I have noticed that the computer seems to stay turned off when there sounds like (just before the computer powers off) - what I can only describe as - a clicking noise. It is as if some device needs to properly shut down to prevent the computer from restarting: As if, this device needs to "click" off. Then everything seems fine. It is still inconsistent, but its more information for you all."
Today, I am not sure about this. Whether something is "clicking" I am not sure; it is hard to tell when SOPB is set to Instant Off because there is, of course, the noise of the power button going in which would happen at the same time as the device "clicking" off. Again, this is just extra information.