Unknown Post/Boot problem.

[Exaco]

Basically after cleaning, swapping GPU or hard shutdown ( sudden electricity shutdown etc ) my PC sometimes doesn't boot properly ( display - No Signal ), but i can sometimes hear boot sounds from OS itself such as Skype and other apps, fans, lights etc works everytime.

Tested and working solution: Turning the PC on/off via the PSU switch ( turning off and after 1sec back on, then i dont need to press the power and PC automatically boots itself ) till it makes some beep or turns off after sec and starts booting again, if beep is there there's like 2 out of 4 chance that display will work and it will post.
Also idk from where the beep is coming, since i lost my speaker somewhere and its not connected to the motherboard ( its more like electrical beep ).

If that issue happens, i have to switch it on/off for like 10mins up to 3hours till it shows some signs, sometimes it goes into boot loop ( on/off on its own ). However after it starts to show display the PC works like new, no issues whatsoever until it gets "hard shutdown" or i clean it with semi-reassembly.

What the problem is not:
It's not the cables.
It's not the GPU.
It's not the Monitor.
It's not the RAM.
It's not the CPU.
It's not the HDMI.
No overheating.

What i think it is:
Faulty Motherboard
Faulty PSU.


Specs:

CPU: Intel® Core™ i5-2320
GPU: ZOTAC GTX 980Ti 6GB AMP! Omega
RAM: 16GB Corsair Vengeance® Low Profile
MB: GIGABYTE H61 - GA-P61-S3
SSD: Samsung 840 EVO 120GB
HDD: Western Digital WD Green 2TB
PSU: OCZ 650W