Question Computer Randomly Shuts Down, sometimes also turns back on?

[Fenius]

so uh recently i had a power outage, and because of the stupid idiot that i am, i left the outlet plugged in with the cable, so after that, my computer started randomly shutting off and turning on, but its not the usual black screen thing, windows LITERALLY says "shutting down.." as if the button was pressed, if anyone could help me with this it would be appreciated.
i suspect one of the these things:
1. it could be the power button/power wires which arent having a great contact, or something is giving a false warning that the computer is shutting down? idk
2.the motherboard has a short circuit probably because its not getting enough power, or something is making it think its gonna shut down (like a signal)
3. the power supply isnt giving continious power, which is unlikely since the computer does boot for a while, sometimes even 3 hours, but randomly shuts down, with WINDOWS LITERALLY INDICATING THAT ITS SHUTTING DOWN. (it also does it when in extreme load i think, sometimes it doesnt even in extreme load, sometimes it does, its just...random.)
are any of my points probably correct? i had a failed hard drive that i forgot to remove, i did remove it now but the issue does still persist.
any help would be appreciated.
my computer is an HP Elitedesk 800 G1 SFF

4x2 (8) GB DDR3 RAM
256 SATA SSD
Intel Core i5-4570
Windows 10

 

[zinkles]

What's your PSU model and how old is it?

 

[Fenius]

What's your PSU model and how old is it?

It's a HP 702307-002 - 240W power supply 12VDC output, 92% efficient, with power factor correction (PFC), i don't know if it had a voltage spike or the motherboard doesn't like it anymore though because, again, windows LITERALLY informs me when my computer shuts down...