Various display glitches and crashes leading up to PC not booting.

So late last month my PC started freezing at random times with various display glitches such as a dark blue screen, vertical grey/white lines, strange red box patterns, thin red horizontal lines, distorted text and a black screen with green and white gibberish text across the whole screen. It would crash regardless if I was running some games, Photoshop, a few browser tabs or even nothing at all. Sometimes they happened after a few hours and sometimes they happened after a few minutes. The first thing I did was reset and reinstall windows, then look up my service tag and made sure to update my BIOS/system drivers/GPU drivers etc. It was still crashing at random over a couple days and I kept my eye on the event viewer to try and figure out what was wrong. I noticed I kept getting the error "AMD display driver has stopped responding and has recovered". I suspected it might be a dust issue on the GPU so I opened up the casing and tried to dust everything the best I could since I hadn't cleaned it in a long time. It still crashed a few times so I just left it alone overnight and tried again the next morning. Surprisingly it was running just fine after that like nothing was wrong.

Fast forward to this Tuesday and my computer froze with vertical grey/white lines across the whole screen. It wasn't recovering on it's own so I had to force shutdown. When I rebooted, the windows logo and welcome text were half dyed in red and froze. I rebooted again and this time it only made it to the starting windows text which froze, was distorted and had thin red horizontal lines crossing through everything. I tried rebooting one more time and it no longer booted at all. The lights turn on, all the fans run, my motherboard doesn't have a speaker installed so I couldn't do a beep test, nothing displayed on my monitor, I left my speakers on to see if I could hear windows starting up but there was nothing, and I noticed that I no longer had to hold the power button for a while to force shutdown since it just turned off the second I pressed it.

So far here is what I've tried:
-Letting the PC cool for half a day (no changes)
-Switching display cables from HDMI to a known working DVI (no changes)
-Dusting all parts more thoroughly (no changes)
-Reseating the GPU (no changes)
-Paperclip test the PSU (still has power)
-Try to boot without GPU (I don't think my PC has an onboard GPU but I did notice that the force shutdown required me to hold the button for a while again rather than turning off instantly)

Going by the stable yellow light on the motherboard I assume it's still getting power, and the casing fan/PSU fan/GPU fan are all running fine. I don't have the tools to get to the CPU to test it and I'll probably buy a speaker for the motherboard to try a beep test soon. I don't have any spare parts to swap with my own to check it that way and money is tight so I can only afford to replace a single part. I've had this PC since 2011 and the only parts I've replaced since then was the PSU and GPU about 3 years ago and they haven't had any issues till now.

Specs:
Model: Dell Inc XPS 8300
OS: Windows 7 Professional
CPU: Intel Core i7-2600 Quad-Core Processor 3.4 GHz
RAM: 8GB 1333MHz DDR3 (upgraded to 16GB I think)
GPU: AMD R9 270 Sapphire
PSU: Thermaltake TR2 600W ATX 12 V2.3
Mobo: Dell XPS 8300 Vostro 460
Hard Drive: 1.8TB installed (don't have the rest of the details)

I've been combing through forum topics and google since this all started but from everything I've read, I still can't pinpoint if the issue is the PSU, GPU, Motherboard or something else entirely. In the meantime before I get a speaker for the motherboard I'd like to know if there's some more tests I could run without needing spare parts or if any of these issues point to something in specific.