@MrTroll did you delete this comment?
The thing that definitely stands out to me in those pics is the CPU fan isn't attached to the heatsink correctly. I don't know if it would even spin up like that, but even if it does it might not be doing an adequate job of cooling the CPU. That might explain why the system powers up and then shuts down after a minute.
Because you were absolutely correct. The way it looks crooked like that was how the manufacturer had it situated for whatever reason from the beginning, because while everything was still working fine and I opened up the case last night, it was in that crooked position.
I used
@murgatroid suggestion and went back to the beginning, removing the new graphics card and power supply to try and pinpoint the issue. I reconnected the old power supply, plugged the HDMI cable into the onboard factory video card, and powered it up. This time, the screen said there was a cooling fan not working.
I was hopeful that we were narrowing down the possible issue while also feeling kinda sad, thinking I just might've broke something else while tinkering, being both inexperienced and dumb.
I powered off and unplugged, checked the little connectors on both fans that plug into the motherboard. They were snug tight, so that was a dead end.
Then I remembered something I did late last night as it was getting really late. I was very tired, getting ready to give up for the night. But for some ungodly reason, I loosened the 4 screws on the CPU fan and removed it. I think I wanted more space to work around. (work around what I don't know, I was very sleepy and starting to get a little confused and delirious.
I saw that removing it did absolutely nothing that would help so I put the 4 screws back in and went to bed.
Since the fans were both connected to the motherboard properly, I checked the 4 screws that secured the CPU fan and wouldn't you know, 2 were a little loose. Somehow I hadn't even noticed the two loose screws with the case removed and the inside exposed.
I tightened them until all 4 screws were snug and tried booting up again with the old power supply and it started up fine, CPU fan again spinning with vigor.
So I try it again with just the new power supply and the factory video card to narrow it down incase a new issue came up. Thankfully the new power supply works fine, the computer started right up.
All that's left now is the new graphics card. I power down, stick it in the slot and plug the previously unused wire from the new power supply into it, start the computer and it starts up fine.
A few setbacks but all in all a decent experience. Thank you to everyone for the helpful suggestions. Even basic info that you may think everyone knows is appreciated, cuz those are the things that ppl tend to overlook, especially a novice like me.
Again, thanks a million! You guys kept me from having to join some stuck up computer forum where they'd probably make passive aggressive comments and treat me with contempt.