i hate to say it...

ram might be fucked, run a memtest to be sure. I would also recommend reinstalling your video drivers and making sure they are the latest.

Really hoping it's not a hardware issue, but what exactly would be the best way to determine which part(s) are the culprit(s)? I guess the first thing to try is to swap the PSU out?

Windows memory diagnostic tool didn't report any errors. Newest GPU drivers have been reinstalled and the issue persists. I also ran Heaven 4.0 and got pretty normal results.

When I had faulty ram windows diagnostic tool never found anything, run memtest86

but I think it's more likely the GPU

Agree with loot, run memtest86. Be prepared to run it overnight as it can take quite a bit of time. Also -- even though it seems silly try switching to a low res like 800x600 then switching back to 1080 right after. This will reset your windows video "profile" to default which helps on occasion.

Do you even have a spare PSU lying around?
Also PSUs are binary: They either deliver power or they don't. If your pc doesn't turn on or randomly turns off you can blame the PSU. If a game thinks your GPU does not support alpha blending with floating point render targets then that's probably not because you're getting 12.01V instead of 12.05V.

Do you actually trust windows to diagnose errors correctly?

Just leave Heaven running overnight to be sure.
If I had to guess I'd say windows is a bit fucked, maybe SSD a bit scrambled (they really don't like power outages) and now there's software bullshit going on. Of course the other option is that your GPU is fucked, which you can test by swapping it out.

inb4 the power outage was an inside job by banny to get a tactical advantage for esea grand finals

run memetest69

Ok so here's where I'm at in terms of testing:
1. Swapped out PSU with my sister's 700w OCZ PSU. The computer boots up (I can hear the normal sounds of booting to the desktop and I can see the home streaming popup from Steam on my laptop) but all my monitors are blank.
2. Swapped back to my normal PSU. The exact same thing as 1. happens.
3. With my normal PSU, pull my GPU out and plug one monitor (DVI) into my motherboard. Everything seems to work fine (it boots and I can see my desktop, launch TF2, etc.).
4. Install my GPU into my dad's PC. Everything seems to work fine.
5. Reinstall GPU into my PC, using a different PCI-E lane. Only one monitor (the same one as 3.) plugged in. Same problem as 1.
6. Swap out GPU power cables from my PSU to the other one that came with the PSU that I have never used (card is 1x 8 pin). Same problem as 1.

So I'm kind of stumped. It seems that the GPU works (worked in my dad's PC), the PSU works (worked when using integrated graphics, also tested with a different PSU and had the same problem), and the monitor works (worked when using integrated graphics), but all together something is messing up. The only thing that I could think of is that all of the PCI-E lanes on my motherboard aren't functioning correctly?

EDIT: Resetting CMOS with my normal PSU plugged in let me boot into Windows and have my monitors display things fine. But the problem in the original post (choppiness) persists. It is worth noting that resetting the CMOS and trying my sister's 700W PSU does not result in my monitors displaying anything, so I guess that PSU isn't working correctly (she hasn't used it in like a year). I'm going to pull my dad's PSU out of his rig and see if my PC starts acting normal again.

I'd doubt it's the PSU if it's turning on and all of your components are turning on - I'd get a nice bright flashlight and look over the board and see if you see anything that looks like it popped or fried, especially anything around your PCIe slots. It could also be an HDD/SSD issue and I imagine you've probably run a chckdsk already - but if you've not at least that's something more to try. If you've still got the manual you may be able to find the full mapping of the board and that could alert you to spots to look in for broken components.

But from the sounds of things it's either some electrical component that routes out of or to your PCIe slots or it's your storage device. I'd give your SATA and etc ports a good look over with a flash light.

Another thing to check is to go through your BIOS pretty extensively - because some boards have brown-out protection that will fiddle with default settings to make sure your computer doesn't kill itself when it receives too little power to run components correctly and perhaps something is being throttled by your BIOS not having come out of brownout protection.

Sometimes with fried components it's hard to really see them if they just popped and didn't fully burn up so using a magnifying glass if you've got one would be a good idea because sometimes the holes in say, something like a capacitor, can be EXTREMELY small with no real sign that anything is wrong externally. On the bright side most electrical components cost less than 10$ - then all you need to know is how to solder things - or know somebody who does. (A 3 Wire Receptacle Tester only costs like 8-10$ and should last you years and years and it will tell you if you're protected or not when used on a power strip - a cheap multimeter is usually around 20-30$ especially if you wait on sales and you can use it for all sorts of fun projects, but the 8-10$ three tester will be more than enough for most people).

I should also point out that although some surge protectors are really cheap (you can pick some up on amazon for 5-6$) typically those extra cheapo surge protectors only survive *one* surge and then their surge protecting capability is gone and you're essentially just using an extension cord. If you invest a lot in your PC it's a good idea to either test your surge protector after every power surge or outage, or buy a fancy one that specifically states it will survive multiple surges (but still test it anyways) - those tend to range in the 40-60$ range, but they tend to have 12+ outlets and all kinds of wacky stuff going on, which is really nice as long as your house can manage having that much crap plugged in at once lol.

To address the blank screens, try booting up in safe mode by spamming f8 as your computer boots up. If successful you can try switching to a simple video configuration such as only enabling 1 monitor using a low resolution then restarting into normal mode to see if that helps.