Computer crashing every 15min. This problem came up overnight

[Microsoft Windows]

I can't figure out if I have a hardware or a software issue (Long Post, lots of information). I will respond quickly I custom-built my pc (specs below) about four years ago. About six months ago, my power supply died. I knew it was my power supply because when I took it out, I could hear a piece rattling around inside. I then went to my local Microcenter and bought a new one. When I plugged it into my computer and turned it on, nothing happened. I tried that new power supply on my friend's computer, and it did not power on anything with his. So, I figured I just got a dead one, ran back and

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