4 short beeps with long intervals at bios splash, after that black screen (no BIOS access)

summotion

Prominent
May 28, 2017
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Hello, after working on my problem for 3 days this is my last resort.
The problem is as follows:
Computer boots up as normal, the splash screen hangs for a solid minute while the PC makes 4 short beeps with long intervals (around 20 sec), after the last beep the computer displays a black screen. I am unable to access the BIOS. It also used to restart quickly before the splash screen, but after resetting CMOS the restart disappeared.
Probable cause:
I was transporting my computer - my friend's dad took the computer off my hands quite heavily so I could hear rocking inside, I thought it was because of one of my HDDs being unsuspended due to the PSU cables not reaching it. After I got home it's not working anymore.

The beeps started when I changed some settings in the BIOS a month or so ago (I nullified the integrated graphics' RAM as it was taking it from my RAM sticks), but the computer managed to start normally.
I've had some problems with my PC before, but they've been quite easy fixes - reseating the GPU & swapping the PSU back and forth have fixed 2 of my recent start-up problems.

What I've tried:
Resetting CMOS by taking out the battery - made the initial restart disappear
Reseating both RAM sticks
Reseating graphics card
Changing SATA ports and cables
Swapping the PSU
Booting up with no SATA cables connected (No HDDs or optical drives)
Plugging the monitor straight into the motherboard ("graphics card error" beep) (did this after resetting the CMOS)

Specs:
Motherboard
GIGABYTE GA-H61M-S2PV
CPU
Intel Core i3-3220 @ 3.2 GHz
RAM
Corsair CMV8GX3M2A1333C9 (8GB x2, DDR3)
GPU
GIGABYTE GTX 750Ti, 2GB (it's powered by a 2x Molex -> 1x 6pin, I know it's a bad idea but I had no other choice, also the cable was included with the card)
PSU
550W (with the 2x Molex -> 1x 6pin setup)
PSU used for swapping
450W (with a real 6pin connector)
SATA
2x HDDs (don't remember the RPMs)
1x optical drive

I'll add more info if needed.