Windows won't load if I have both my new Wireless network card in and my graphics card.

Hello!

I just moved and had to buy a wireless network card (AC1900 Wireless Dual Band PCI Express Adapter). However, when I uninstalled it, Windows (Windows 10) wouldn't boot and would show red lines in the Windows loading screen: https://drive.google.com/open?id=1jPUhpv1-UJ5Ll9GYxPHY1b5T31WjMKUq8g

So I took multiple steps trying to find a way to make this work. If I disconnect my graphics card (GTX 980 TI) and plugged my monitor to the onboard graphics card, Windows would boot up and I could install the drivers for my new wireless network card and it would work great. Now if I tried to reconnect my graphics card, Windows wouldn't boot up again.
If I unplugged the wireless network card but had the graphics card plugged in, then Windows would boot up again...

I then tried reinstalling Windows, which worked with both connected. After a while of downloading the updates for Windows, it did it again, but this time the screen just went black and had the red lines: https://drive.google.com/open?id=1oZMQtlP2ZIdp150uFdFMP5FMnDbOoCGdaw (notice no Windows logo)

If I have them both connected, and force shut down the computer after the red lines appear, Windows would do the "Diagnosing PC" thing and I tried the option that tried fixing startup issues. Which worked for a bit, Windows booted up and then after 2 minutes it the screen would go black again with the red lines.

I also tried another slot for the wireless network card, same problem.

So I don't know, it seems it's one or the other (Graphics card vs Wireless Network Card). Could it be my power supply that doesn't provide enough power for both components?

I have other problems that may be of help here related to my computer. The PCI slot where my graphics card is lacks the little plastic thing that keeps it in place, so my graphics card is flimsily placed and if I touched it could disconnect the graphics card. I tried installing the graphics card to another slot that had the plastic latch thing, but my computer wouldn't seem to use the graphics card then, if I disconnected the monitor from in and plugged it in the onboard graphics card, it would show that my computer were using the onboard graphics card instead. So is this an indication that something is wrong with my motherboard?

Now though, my computer just won't boot up at all, but that has happened multiple times before (couple times a year, mostly when I move my computer around) and would resolve on its own. I don't know if you can make sense of it, and maybe now it just won't boot up anymore

Here are the specs for my computer:
Motherboard: Gigabyte Z87X-D3H
Graphics Card: Nvidia GTX 980 TI (Nvidia manufactured)
RAM: 8 gb
Power supply: Thermaltake TR2 RX 750W
Wireless Network Card: AC1900 Wireless Dual Band PCI Express Adapter
CPU: Intel i7-4770k (@ Base clock)
CPU Cooler: Corsair H100i (mentioning in case of power needs maybe?)

So since my computer still isn'it booting, I'm thinking of taking everything out and putting everything back in again, I don't know, maybe the back of my motherboard is touching the case where it shouldn't? Honestly I'd like advice from people that know more than me and to know what my next steps should be.

Thank you very much for reading!