Why does my PC shut down randomly?

I have a custom made Desktop PC which recently started switching off suddenly for no apparent reason. I am able to turn the computer back on immediately. Sometimes it can take a few hours untill the PC turns off, sometimes it does so on startup. I have tried using a different power supply and the problem still... show more I have a custom made Desktop PC which recently started switching off suddenly for no apparent reason. I am able to turn the computer back on immediately. Sometimes it can take a few hours untill the PC turns off, sometimes it does so on startup. I have tried using a different power supply and the problem still persists. I also attempted moving the ram around (in all slots and: with just the one stick as well as both together). I also used another hard drive (removed all previous drives and tested different sata ports) but the problem still persists.

My components are as follows:
Mother board: Gigabyte GA-B75M-D3H
Power supply: Hutntkey APFC 600, 600W
CPU: Intel i7 3770
RAM: 2 x Transcend 4GB DDR3 1600 DIMM CL11
SSD: Samsung 750 EVO 250GB

What could I still do to troubleshoot/ fix the problem?
My power supply makes a weak high-pitched sound even when switched off. Could this, over time, have damaged something on the MB?

All answers would be greatly appreciated.
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