PC keeps rebooting in a loop until I pull the plug

So, here’s the deal. I’ve got this PC that’s about 4 years old now. It’s actually a pretty solid machine—fast, reliable, and hasn't given me any trouble until yesterday... Now, when I hit the power button, it stays on for maybe 3 seconds before just cutting out. Then, after a few seconds, it tries to boot up again, only to shut down yet again. It seems to have calmed down for the moment and is running fine, at least for right now... But man, what could be causing that?

Right now, my best guess is either a failing power supply or just a massive buildup of dust. If I were in your shoes, I'd pop the case open—if you have some canned air handy, give everything a really thorough cleaning. Once that's done, fire it up and just let it run for a bit. If the same issue keeps popping up after the cleanup, maybe see if a buddy can lend you a spare PSU to test? That way you'll know for sure if yours is shot before you go out and buy a new one. By the way, you might want to grab a tool like CPU-Z to keep an eye on those temperatures... http://www.cpuid.com/softwares/hwmonitor.html If you want, grab a screenshot of the readings so we can take a look together.

It's possible you're dealing with a faulty power supply cable; I actually ran into a nearly identical issue myself once.

The PSU is an LC Power 380W

It was brand new when I bought it $50

A buddy of mine has some much weaker gear, so I'm a little nervous about plugging this in. Here’s my current setup:

CPU: Intel Core i5-6500 dual core 3.2GHz
GPU: ATI Radeon HD 4500 1GB
4GB RAM
Two hard drives
And 3 fans
Plus, who knows what else is pulling power—webcam, external drive, and all sorts of random stuff plugged into the USB ports

The power button on the case might just be acting up. I’d say try swapping it out with a reset cable and its corresponding switch to test things. If everything runs smoothly after that, you've found your culprit.