Good suggestion Pretzal - I don't use "non-name" power-supplies off the shelf for a good reason. Buy a "name" brand with an over-generous wattage.
But this scenario stirs another painful memory.
Some years ago I had a DOS machine that began restarting at times for no reason that I could see. No obvious pattern.
Eventually (several useless reinstalls and much hair-ripping later) tracked it down to
an intermittent short in the reset switch on the case....
And I remember a similar problem that in the end turned out to be a duff connector shorting in a floppy cable
And another that finally proved to be a sticky key on the keyboard.
It isn't always the software.
Oh, and I've said it once and I'll say it again. Many instabilities are due to marginal memory or "off" memory timings or bad BIOS settings (overclocks etc.).
Memtest has to run overnight without errors before you can trust the machine.