I just had a new idea on what could be wrong. When the computer starts it draws a lot of power. This will in turn make the voltage drop for a short while if your power supply (for the house, not the PSU) is heavily loaded compared to how much it can handle. If the voltage drops below the minimum needed for the computer it dies.
What you can do about it... well you can shorten the length of wire between the fusebox and the computer (like using a different power outlet and no extension cord) or you can use an UPS. However I would be more concern... (
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