Goowpea

You could try removing the CMOS baterry from your MOBO for couple of seconds to see if resetting the BIOS will help (or clear CMOS with the button on your motherboard if you have one).
 
You could also try updating the BIOS, but check the notes for the BIOS to see if it's not going to obsolete your CPU or RAM. 

From the picture I see that the rest og the jack sticks out a little bit from the socket. Try putting little bit sort of super glue on toothpick (drop would be too much) and touch the connector fragment with it. Hold for a sec for gluue to harden and pull it out. BE EXTREMELY CAREFUL NOT TO GLUE THE JACK TO THE SOCKET 'CAUSE IN THAT CASE YOU'D BE EXTREMELY F****D.

Did you OC-ed that GPU? Install their OC software and check the fans curve. In my built I had a problem with my GPu crahing when the fans were spinning too slow. I wasn't turning of my screen but I was receiving drivers crashes. I changed the fans speed to be at 20% at the lowest and now it's working fine.

I'd recommend you Creative headsets. Creative is producing music equipment for something like 15 years and they know what they are doing. You need to check if it's compatible with PS4. My friend is using this one Creative Labs CREATIVE HS-430 Gaming Headset. I can hear him like he's sitting right next to me. I've heard that there's sometimes problem with detachable mic in that particular model, but you can look for headsets with nondetachable mics. Sound Blaster Tactic3D Fury should be fine it's compatible with PS4 - altough it has detachable mic. You can also check some Steelseries, Razer or Logitech products but they are pricey and personally I'm not convenced about their sound products. Keyboards and mices are awesome but I've heard mixed opinions 'bout headsets.

Loose screw mounting the MOBO to the case shouldn't be a problem. They're not required. Some cases are mounted on some sort of plastic latches. I think that is caused by loose screw. The MOBO was bending all this time and something like one path on it or some solter might have broke. It's hard to tell. Try disassembling your PC and assemble it on your MOBO box or some flat nonconductive surface.

Format your SSD with the stick you burned the image onto. If you want to try Linux go LiveCD first. You can always buy new windows if your copy is not working. TBH I've never had a problem with installing OEM windows in different setup so you can try just reinstalling it with youur serial key. 
 
AND BTW when you're changing MOBO and everything you always install new fresh copy of OS. It doesn't matter if it's Linux SteamOS or Win.

For me it looks like some sort of RAM issue. You can check the HDD by unplugging it and turning the PC on. It should at least boot up into BIOS. If you have two memory sticks you can unplug one and try to turn it on. You can swapping memory slots. Also try different PSU. If that doesn't help it's probably CPU or MOBO. TBH I don't know how to test GPU. You can always try different one, but I think it'll be hard to get. 

I stand corrected. In my defense I wasn't trying to be a douche, I tried to help.

I think what he is asking is if it will be good for cuda enabled rendering. In which case the gpu will actually make a difference in rendering times. But to answer the question he asked, yes it will be great for video editing with cuda enabled. Hope that helps!

Yes? Why wouldn't you be able to do that. GPU is device that is able to display images on your monitor (this definition is really simplified). It's not limitting any functionality of external devices. That limitations depends on drivers and I've never heard that display drivers had a conflict with a image/movie editor.You can lack drivers or programs but GPU itself doesn't limit your options. 
 
If you're building your first PC and you didn't know that, built it with help of someone more experienced. otherwise you can lost yourself in all that. I'm not trying to be rude or something. Take this as a good advice.

You want to boot into bios without CPU? I got it right?